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How to find the missing sides notes and examples

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Basic Trig Ratios Intro Lesson

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How to find the missing sides notes and examples

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Basic Trig Ratios Intro Lesson

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Two triangles are congruent if they have:

exactly the same three sides and

exactly the same three angles.

But we don't have to know all three sides and all three angles ...usually three out of the six is enough.

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS (side, side, side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

For example:

is congruent to:

(See Solving SSS Triangles to find out more)
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side)

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

For example:
(See Solving SAS Triangles to find out more)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle)

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

For example:
(See Solving ASA Triangles to find out more)
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side)

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.

For example:
(See Solving AAS Triangles to find out more)
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg)

This one applies only to right angled-triangles!

or

HL stands for " Hypotenuse, L eg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

the same length of hypotenuse and

the same length for one of the other two legs.

It doesn't matter which leg since the triangles could be rotated.

For example:
(See Pythagoras' Theorem to find out more)
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Caution! Don't Use "AAA"

AAA means we are given all three angles of a triangle, but no sides.
This is not enough information to decide if two triangles are congruent!
Because the triangles can have the same angles but be different sizes:

Without knowing at least one side, we can't be sure if two triangles are congruent.

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Two triangles are congruent if they have: exactly the same three sides and exactly the same three angles. But we don't have to know all three sides and all three angles ...usually three out of the six is enough. There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

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Preparing Congruent Triangle Proofs - MathBitsNotebook(Geo - CCSS Math)

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MathBitsNotebook Geometry CCSS Lessons and Practice is a free site for students (and teachers) studying high school level geometry under the Common Core State Standards.

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Maths Tutorial: Trigonometry SOH CAH TOA (trigonometric ratios)

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Trigonometry: Solving Right Triangles... How? (NancyPi)

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Basic Trigonometry: Sin Cos Tan (NancyPi)

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Missing Measurements for Similar Triangles

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Finding unknown lengths of sides of similar triangles

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Triangle Similarity - SSS, SAS, and AA 128-2.28

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Triangle Congruence Theorems, Two Column Proofs, SSS, SAS, ASA, AAS Postulates, Geometry  Problems

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Proof Problems for Similar Triangles - MathBitsNotebook(Geo - CCSS Math)

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MathBitsNotebook Geometry CCSS Lessons and Practice is a free site for students (and teachers) studying high school level geometry under the Common Core State Standards.

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Maths Tutorial: Trigonometry Law of Sines / Sine Rule

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Using Trig Ratios to find Angle Measures

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Trigonometry - Finding angles Worksheets

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To find angles, we can use what are known as inverse trigonometric functions. On your calculator, the inverse trig functions will appear as SIN-1, COS-1, or TAN-1. The output of these functions should always be understood as angles.

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Colin Dodds - Pythagorean Theorem (Math Song)