Theorems- From Discovery to Prescribed Proofs: JC:4,6,9,14 &19 and LC: 11,12,13 by Mr Downes' Padlets https://padlet.com/rdownes/theorem Strand 2: Geometry and Trigonometry. Theorems- From Discovery to Prescribed Proofs: JC:4,6,9,14 &19 and LC: 11,12,13. A theorem is a statement deduced by logical argument from the five axioms and other theorems that come earlier in the logical sequence. en-us 2020-03-29 21:42:05 UTC 2025-12-07 02:01:41 UTC hello@padlet.com rdownes https://padlet.com/rdownes/theorem/wish/503553227 2020-04-12 14:54:13 UTC https://padlet.com/rdownes/theorem/wish/503553227 rdownes https://padlet.com/rdownes/theorem/wish/503579474 2020-04-12 15:22:39 UTC https://padlet.com/rdownes/theorem/wish/503579474 rdownes https://padlet.com/rdownes/theorem/wish/503580696 2020-04-12 15:24:29 UTC https://padlet.com/rdownes/theorem/wish/503580696 11- three parallel lines cut off rdownes https://padlet.com/rdownes/theorem/wish/503583347 2020-04-12 15:28:32 UTC https://padlet.com/rdownes/theorem/wish/503583347 11- three parallel lines cut off rdownes https://padlet.com/rdownes/theorem/wish/503583348 2020-04-12 15:28:33 UTC https://padlet.com/rdownes/theorem/wish/503583348 10. diagonals bisection rdownes https://padlet.com/rdownes/theorem/wish/503583751 2020-04-12 15:29:08 UTC https://padlet.com/rdownes/theorem/wish/503583751 Change "Last modified" to "Title" and scroll for Theorems, Axioms ( Some Broken Links!) and corrolaries rdownes https://padlet.com/rdownes/theorem/wish/503584304 2020-04-12 15:30:06 UTC https://padlet.com/rdownes/theorem/wish/503584304 1 Opposite Angles Equality rdownes https://padlet.com/rdownes/theorem/wish/503609996 2020-04-12 16:09:42 UTC https://padlet.com/rdownes/theorem/wish/503609996 1 Opposite Angles Equality rdownes https://padlet.com/rdownes/theorem/wish/503610324 2020-04-12 16:10:10 UTC https://padlet.com/rdownes/theorem/wish/503610324 rdownes https://padlet.com/rdownes/theorem/wish/503611358 2020-04-12 16:11:43 UTC https://padlet.com/rdownes/theorem/wish/503611358 2 Isos Tri Opp Equalities rdownes https://padlet.com/rdownes/theorem/wish/503612536 2020-04-12 16:13:39 UTC https://padlet.com/rdownes/theorem/wish/503612536 ...2 Isos Tri Opp Equalities rdownes https://padlet.com/rdownes/theorem/wish/503612543 2020-04-12 16:13:40 UTC https://padlet.com/rdownes/theorem/wish/503612543 2 Isos Tri Opp Equalities rdownes https://padlet.com/rdownes/theorem/wish/503612888 2020-04-12 16:14:16 UTC https://padlet.com/rdownes/theorem/wish/503612888 ...3. (Alternate Angles). rdownes https://padlet.com/rdownes/theorem/wish/503615143 2020-04-12 16:17:41 UTC https://padlet.com/rdownes/theorem/wish/503615143 3. (Alternate Angles). rdownes https://padlet.com/rdownes/theorem/wish/503615146 2020-04-12 16:17:41 UTC https://padlet.com/rdownes/theorem/wish/503615146 ...3. (Alternate Angles).... rdownes https://padlet.com/rdownes/theorem/wish/503615147 2020-04-12 16:17:41 UTC https://padlet.com/rdownes/theorem/wish/503615147 3. (Alternate Angles). rdownes https://padlet.com/rdownes/theorem/wish/503615532 2020-04-12 16:18:05 UTC https://padlet.com/rdownes/theorem/wish/503615532 4 (Angle Sum 180). rdownes https://padlet.com/rdownes/theorem/wish/503616892 2020-04-12 16:19:53 UTC https://padlet.com/rdownes/theorem/wish/503616892 ... 4 (Angle Sum 180). rdownes https://padlet.com/rdownes/theorem/wish/503616899 2020-04-12 16:19:53 UTC https://padlet.com/rdownes/theorem/wish/503616899 4 (Angle Sum 180). The angles in any triangle add to 180 rdownes https://padlet.com/rdownes/theorem/wish/503617377 2020-04-12 16:20:38 UTC https://padlet.com/rdownes/theorem/wish/503617377 5 (Corresponding Angles). rdownes https://padlet.com/rdownes/theorem/wish/503617852 2020-04-12 16:21:25 UTC https://padlet.com/rdownes/theorem/wish/503617852 ... 5 (Corresponding Angles). rdownes https://padlet.com/rdownes/theorem/wish/503617855 2020-04-12 16:21:25 UTC https://padlet.com/rdownes/theorem/wish/503617855 5 (Corresponding Angles). rdownes https://padlet.com/rdownes/theorem/wish/503618775 2020-04-12 16:22:42 UTC https://padlet.com/rdownes/theorem/wish/503618775 6 (Exterior Angle) rdownes https://padlet.com/rdownes/theorem/wish/503620602 2020-04-12 16:25:04 UTC https://padlet.com/rdownes/theorem/wish/503620602 6 (Exterior Angle) rdownes https://padlet.com/rdownes/theorem/wish/503620957 2020-04-12 16:25:38 UTC https://padlet.com/rdownes/theorem/wish/503620957 ...7 greater angle side pairings rdownes https://padlet.com/rdownes/theorem/wish/503621588 2020-04-12 16:26:23 UTC https://padlet.com/rdownes/theorem/wish/503621588 ...7 greater angle side pairings rdownes https://padlet.com/rdownes/theorem/wish/503621592 2020-04-12 16:26:23 UTC https://padlet.com/rdownes/theorem/wish/503621592 ...7 greater angle side pairings rdownes https://padlet.com/rdownes/theorem/wish/503621594 2020-04-12 16:26:23 UTC https://padlet.com/rdownes/theorem/wish/503621594 ...7 greater angle side pairings rdownes https://padlet.com/rdownes/theorem/wish/503622045 2020-04-12 16:27:07 UTC https://padlet.com/rdownes/theorem/wish/503622045 ...8 Two sides greater than rdownes https://padlet.com/rdownes/theorem/wish/503623032 2020-04-12 16:28:35 UTC https://padlet.com/rdownes/theorem/wish/503623032 8 Two sides greater rdownes https://padlet.com/rdownes/theorem/wish/503623039 2020-04-12 16:28:36 UTC https://padlet.com/rdownes/theorem/wish/503623039 8 Two sides greater than the third. rdownes https://padlet.com/rdownes/theorem/wish/503623391 2020-04-12 16:28:58 UTC https://padlet.com/rdownes/theorem/wish/503623391 9. Prlgrm opps equalities rdownes https://padlet.com/rdownes/theorem/wish/503624658 2020-04-12 16:30:59 UTC https://padlet.com/rdownes/theorem/wish/503624658 9. Prlgrm opps equalities rdownes https://padlet.com/rdownes/theorem/wish/503624835 2020-04-12 16:31:18 UTC https://padlet.com/rdownes/theorem/wish/503624835 10. diagonals bisection rdownes https://padlet.com/rdownes/theorem/wish/503628815 2020-04-12 16:38:01 UTC https://padlet.com/rdownes/theorem/wish/503628815 10. diagonals bisection rdownes https://padlet.com/rdownes/theorem/wish/503628818 2020-04-12 16:38:01 UTC https://padlet.com/rdownes/theorem/wish/503628818 11- three parallel lines cut off rdownes https://padlet.com/rdownes/theorem/wish/503629095 2020-04-12 16:38:30 UTC https://padlet.com/rdownes/theorem/wish/503629095 rdownes https://padlet.com/rdownes/theorem/wish/503643239 2020-04-12 17:01:03 UTC https://padlet.com/rdownes/theorem/wish/503643239 rdownes https://padlet.com/rdownes/theorem/wish/503643250 2020-04-12 17:01:03 UTC https://padlet.com/rdownes/theorem/wish/503643250 rdownes https://padlet.com/rdownes/theorem/wish/503643251 2020-04-12 17:01:03 UTC https://padlet.com/rdownes/theorem/wish/503643251 rdownes https://padlet.com/rdownes/theorem/wish/503643252 2020-04-12 17:01:03 UTC https://padlet.com/rdownes/theorem/wish/503643252 rdownes https://padlet.com/rdownes/theorem/wish/503643254 2020-04-12 17:01:04 UTC https://padlet.com/rdownes/theorem/wish/503643254 rdownes https://padlet.com/rdownes/theorem/wish/503643255 2020-04-12 17:01:04 UTC https://padlet.com/rdownes/theorem/wish/503643255 rdownes https://padlet.com/rdownes/theorem/wish/503643256 2020-04-12 17:01:04 UTC https://padlet.com/rdownes/theorem/wish/503643256 rdownes https://padlet.com/rdownes/theorem/wish/503643258 2020-04-12 17:01:04 UTC https://padlet.com/rdownes/theorem/wish/503643258 rdownes https://padlet.com/rdownes/theorem/wish/503646220 2020-04-12 17:06:01 UTC https://padlet.com/rdownes/theorem/wish/503646220 rdownes https://padlet.com/rdownes/theorem/wish/503646226 2020-04-12 17:06:01 UTC https://padlet.com/rdownes/theorem/wish/503646226 rdownes https://padlet.com/rdownes/theorem/wish/503646239 2020-04-12 17:06:03 UTC https://padlet.com/rdownes/theorem/wish/503646239 rdownes https://padlet.com/rdownes/theorem/wish/503646240 2020-04-12 17:06:03 UTC https://padlet.com/rdownes/theorem/wish/503646240 rdownes https://padlet.com/rdownes/theorem/wish/503646241 2020-04-12 17:06:03 UTC https://padlet.com/rdownes/theorem/wish/503646241 rdownes https://padlet.com/rdownes/theorem/wish/503646250 2020-04-12 17:06:04 UTC https://padlet.com/rdownes/theorem/wish/503646250 rdownes https://padlet.com/rdownes/theorem/wish/503648289 2020-04-12 17:09:29 UTC https://padlet.com/rdownes/theorem/wish/503648289 rdownes https://padlet.com/rdownes/theorem/wish/503648290 2020-04-12 17:09:29 UTC https://padlet.com/rdownes/theorem/wish/503648290 rdownes https://padlet.com/rdownes/theorem/wish/503648291 2020-04-12 17:09:29 UTC https://padlet.com/rdownes/theorem/wish/503648291 12-trespassing parallel line across triangle ratio rdownes https://padlet.com/rdownes/theorem/wish/503655843 2020-04-12 17:21:29 UTC https://padlet.com/rdownes/theorem/wish/503655843 12-trespassing rdownes https://padlet.com/rdownes/theorem/wish/503655977 2020-04-12 17:21:42 UTC https://padlet.com/rdownes/theorem/wish/503655977 12-trespassing rdownes https://padlet.com/rdownes/theorem/wish/503655990 2020-04-12 17:21:43 UTC https://padlet.com/rdownes/theorem/wish/503655990 Theorem 13 rdownes https://padlet.com/rdownes/theorem/wish/503657098 2020-04-12 17:23:38 UTC https://padlet.com/rdownes/theorem/wish/503657098 Theorem 13 rdownes https://padlet.com/rdownes/theorem/wish/503657223 13. If two triangles ABC and A'B'C' are similar, then theirs ides are proportional, in order:]]> 2020-04-12 17:23:51 UTC https://padlet.com/rdownes/theorem/wish/503657223 14 Pythagoras RA triangle squares rule rdownes https://padlet.com/rdownes/theorem/wish/503662964 2020-04-12 17:33:10 UTC https://padlet.com/rdownes/theorem/wish/503662964 14 Pythagoras RA triangle squares rule rdownes https://padlet.com/rdownes/theorem/wish/503663088 2020-04-12 17:33:23 UTC https://padlet.com/rdownes/theorem/wish/503663088 15 (Converse to Pythagoras). rdownes https://padlet.com/rdownes/theorem/wish/503682234 2020-04-12 18:05:32 UTC https://padlet.com/rdownes/theorem/wish/503682234 15 rdownes https://padlet.com/rdownes/theorem/wish/503682541 2020-04-12 18:06:05 UTC https://padlet.com/rdownes/theorem/wish/503682541 16-Pairing Area Conservation rdownes https://padlet.com/rdownes/theorem/wish/503682982 2020-04-12 18:06:54 UTC https://padlet.com/rdownes/theorem/wish/503682982 rdownes https://padlet.com/rdownes/theorem/wish/503685213 2020-04-12 18:11:05 UTC https://padlet.com/rdownes/theorem/wish/503685213 rdownes https://padlet.com/rdownes/theorem/wish/503685217 2020-04-12 18:11:05 UTC https://padlet.com/rdownes/theorem/wish/503685217 rdownes https://padlet.com/rdownes/theorem/wish/503686715 2020-04-12 18:13:43 UTC https://padlet.com/rdownes/theorem/wish/503686715 rdownes https://padlet.com/rdownes/theorem/wish/503686873 2020-04-12 18:14:00 UTC https://padlet.com/rdownes/theorem/wish/503686873 rdownes https://padlet.com/rdownes/theorem/wish/503688276 2020-04-12 18:16:26 UTC https://padlet.com/rdownes/theorem/wish/503688276 rdownes https://padlet.com/rdownes/theorem/wish/503688419 2020-04-12 18:16:41 UTC https://padlet.com/rdownes/theorem/wish/503688419 19-inscribed/centre angle rdownes https://padlet.com/rdownes/theorem/wish/503688520 2020-04-12 18:16:53 UTC https://padlet.com/rdownes/theorem/wish/503688520 rdownes https://padlet.com/rdownes/theorem/wish/503688626 2020-04-12 18:17:04 UTC https://padlet.com/rdownes/theorem/wish/503688626 rdownes https://padlet.com/rdownes/theorem/wish/503688631 2020-04-12 18:17:04 UTC https://padlet.com/rdownes/theorem/wish/503688631 rdownes https://padlet.com/rdownes/theorem/wish/503690028 2020-04-12 18:19:35 UTC https://padlet.com/rdownes/theorem/wish/503690028 rdownes https://padlet.com/rdownes/theorem/wish/503690171 2020-04-12 18:19:50 UTC https://padlet.com/rdownes/theorem/wish/503690171 rdownes https://padlet.com/rdownes/theorem/wish/503690173 2020-04-12 18:19:50 UTC https://padlet.com/rdownes/theorem/wish/503690173 rdownes https://padlet.com/rdownes/theorem/wish/503690177 2020-04-12 18:19:51 UTC https://padlet.com/rdownes/theorem/wish/503690177 Corollaries to 19 rdownes https://padlet.com/rdownes/theorem/wish/503710495 Corollary 2 to Theorem 19

https://www.geogebra.org/m/w6zAXwHJ
orollary 3 to Theorem 19

Corollary 4 to Theorem 19

https://www.geogebra.org/m/JMgjx686

Corollary 5 to Theorem 19

https://www.geogebra.org/m/Kp5JWxhh

]]> 2020-04-12 18:54:58 UTC https://padlet.com/rdownes/theorem/wish/503710495 Corollary 1 to Theorem 10 rdownes https://padlet.com/rdownes/theorem/wish/503712714 https://www.geogebra.org/m/jGNMeAqu]]> 2020-04-12 18:58:44 UTC https://padlet.com/rdownes/theorem/wish/503712714 Corollary 6 to Theorem 20 rdownes https://padlet.com/rdownes/theorem/wish/503713225 https://www.geogebra.org/m/nbvttuJs]]> 2020-04-12 18:59:44 UTC https://padlet.com/rdownes/theorem/wish/503713225 rdownes https://padlet.com/rdownes/theorem/wish/503723183 2020-04-12 19:16:54 UTC https://padlet.com/rdownes/theorem/wish/503723183 rdownes https://padlet.com/rdownes/theorem/wish/503723195 2020-04-12 19:16:55 UTC https://padlet.com/rdownes/theorem/wish/503723195 rdownes https://padlet.com/rdownes/theorem/wish/503777486 2020-04-12 21:00:38 UTC https://padlet.com/rdownes/theorem/wish/503777486 rdownes https://padlet.com/rdownes/theorem/wish/505289819 2020-04-13 21:32:40 UTC https://padlet.com/rdownes/theorem/wish/505289819 rdownes https://padlet.com/rdownes/theorem/wish/505292481 2020-04-13 21:35:19 UTC https://padlet.com/rdownes/theorem/wish/505292481 rdownes https://padlet.com/rdownes/theorem/wish/505298252 2020-04-13 21:41:25 UTC https://padlet.com/rdownes/theorem/wish/505298252 rdownes https://padlet.com/rdownes/theorem/wish/506927871 2020-04-14 17:17:21 UTC https://padlet.com/rdownes/theorem/wish/506927871 rdownes https://padlet.com/rdownes/theorem/wish/511630635 2020-04-16 20:51:13 UTC https://padlet.com/rdownes/theorem/wish/511630635 rdownes https://padlet.com/rdownes/theorem/wish/513181971 2020-04-17 15:48:32 UTC https://padlet.com/rdownes/theorem/wish/513181971 rdownes https://padlet.com/rdownes/theorem/wish/513189460 2020-04-17 15:51:33 UTC https://padlet.com/rdownes/theorem/wish/513189460 rdownes https://padlet.com/rdownes/theorem/wish/514781815 2020-04-18 22:42:02 UTC https://padlet.com/rdownes/theorem/wish/514781815 rdownes https://padlet.com/rdownes/theorem/wish/514782463 TheoremsandProofs
https://padlet.com/rdownes/axiom
https://padlet.com/rdownes/t
https://padlet.com/rdownes/corollary
https://padlet.com/rdownes/converse
https://padlet.com/rdownes/construction
https://padlet.com/rdownes/induction
https://padlet.com/rdownes/t1
https://padlet.com/rdownes/t2
https://padlet.com/rdownes/t3
https://padlet.com/rdownes/t4
https://padlet.com/rdownes/t5
https://padlet.com/rdownes/t6
https://padlet.com/rdownes/t7
https://padlet.com/rdownes/t8
https://padlet.com/rdownes/t9
https://padlet.com/rdownes/t10
https://padlet.com/rdownes/t11
https://padlet.com/rdownes/t12
https://padlet.com/rdownes/t13
https://padlet.com/rdownes/t14
https://padlet.com/rdownes/t15
https://padlet.com/rdownes/t16
https://padlet.com/rdownes/t17
https://padlet.com/rdownes/t18
https://padlet.com/rdownes/t19
https://padlet.com/rdownes/t20
https://padlet.com/rdownes/t21
Axioms
https://padlet.com/rdownes/axiom
https://padlet.com/rdownes/a1
https://padlet.com/rdownes/a2
https://padlet.com/rdownes/a3
https://padlet.com/rdownes/a4
https://padlet.com/rdownes/a5
Corollary
https://padlet.com/rdownes/corollary
https://padlet.com/rdownes/cr1
https://padlet.com/rdownes/cr2
https://padlet.com/rdownes/cr3
https://padlet.com/rdownes/cr4
https://padlet.com/rdownes/cr5
https://padlet.com/rdownes/cr6
Constructions
https://padlet.com/rdownes/construction
https://padlet.com/rdownes/c1
https://padlet.com/rdownes/c2
https://padlet.com/rdownes/c3
https://padlet.com/rdownes/c4
https://padlet.com/rdownes/c5
https://padlet.com/rdownes/c6
https://padlet.com/rdownes/c7
https://padlet.com/rdownes/c8
https://padlet.com/rdownes/c9
https://padlet.com/rdownes/c10
https://padlet.com/rdownes/c11
https://padlet.com/rdownes/c12
https://padlet.com/rdownes/c13
https://padlet.com/rdownes/c14
https://padlet.com/rdownes/c15
https://padlet.com/rdownes/c16
https://padlet.com/rdownes/c17
https://padlet.com/rdownes/c18
https://padlet.com/rdownes/c19
https://padlet.com/rdownes/c20
https://padlet.com/rdownes/c21
https://padlet.com/rdownes/c22
Senior Cycle
1. Statistics and Probability
https://padlet.com/rdownes/lcm10
https://padlet.com/rdownes/lcm11
https://padlet.com/rdownes/lcm12
https://padlet.com/rdownes/lcm13
https://padlet.com/rdownes/lcm14
https://padlet.com/rdownes/lcm15
https://padlet.com/rdownes/lcm16
https://padlet.com/rdownes/lcm16h
https://padlet.com/rdownes/lcm17
2. Geometry and Trigonometry
https://padlet.com/rdownes/lcm20
https://padlet.com/rdownes/lcm21
https://padlet.com/rdownes/lcm22
https://padlet.com/rdownes/lcm23
https://padlet.com/rdownes/lcm24
3. Number
https://padlet.com/rdownes/lcm30
https://padlet.com/rdownes/lcm31
https://padlet.com/rdownes/lcm32
https://padlet.com/rdownes/lcm33
https://padlet.com/rdownes/lcm34
4. Algebra
https://padlet.com/rdownes/lcm40
https://padlet.com/rdownes/lcm41
https://padlet.com/rdownes/lcm42
https://padlet.com/rdownes/lcm43
https://padlet.com/rdownes/lcm44
5. Functions
https://padlet.com/rdownes/lcm50
https://padlet.com/rdownes/lcm51
https://padlet.com/rdownes/lcm52
JuniorCycle
Unifying Strand
https://padlet.com/rdownes/u
https://padlet.com/rdownes/u1
https://padlet.com/rdownes/u2
https://padlet.com/rdownes/u3
https://padlet.com/rdownes/u4
https://padlet.com/rdownes/u5
https://padlet.com/rdownes/u6
https://padlet.com/rdownes/u7
https://padlet.com/rdownes/u8
https://padlet.com/rdownes/u9
https://padlet.com/rdownes/u10
https://padlet.com/rdownes/u11
https://padlet.com/rdownes/u12
https://padlet.com/rdownes/u13
Number Strand
https://padlet.com/rdownes/n
https://padlet.com/rdownes/n1
https://padlet.com/rdownes/n2
https://padlet.com/rdownes/n3
https://padlet.com/rdownes/n4
https://padlet.com/rdownes/n5
2. Geometry and Trigonometry
https://padlet.com/rdownes/gt
https://padlet.com/rdownes/gt1
https://padlet.com/rdownes/gt2
https://padlet.com/rdownes/gt3
https://padlet.com/rdownes/gt4
https://padlet.com/rdownes/gt5
https://padlet.com/rdownes/gt6
Algebra and Functions Strand
https://padlet.com/rdownes/af
https://padlet.com/rdownes/af1
https://padlet.com/rdownes/af2
https://padlet.com/rdownes/af3
https://padlet.com/rdownes/af4
https://padlet.com/rdownes/af5
https://padlet.com/rdownes/af6
https://padlet.com/rdownes/af7
Statistics and Probability Strand
https://padlet.com/rdownes/sp
https://padlet.com/rdownes/sp1
https://padlet.com/rdownes/sp2
https://padlet.com/rdownes/sp3]]> 2020-04-18 22:43:37 UTC https://padlet.com/rdownes/theorem/wish/514782463 rdownes https://padlet.com/rdownes/theorem/wish/515378944 2020-04-19 13:31:16 UTC https://padlet.com/rdownes/theorem/wish/515378944 rdownes https://padlet.com/rdownes/theorem/wish/515379842 2020-04-19 13:32:07 UTC https://padlet.com/rdownes/theorem/wish/515379842 rdownes https://padlet.com/rdownes/theorem/wish/515387464 2020-04-19 13:38:22 UTC https://padlet.com/rdownes/theorem/wish/515387464 rdownes https://padlet.com/rdownes/theorem/wish/520847843 2020-04-21 16:50:43 UTC https://padlet.com/rdownes/theorem/wish/520847843 rdownes https://padlet.com/rdownes/theorem/wish/537729924 2020-04-28 23:07:06 UTC https://padlet.com/rdownes/theorem/wish/537729924