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SD 2.4

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How Do You Find the Measures of Exterior Angles of a Polygon if You Know the Interior Angles? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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How Do You Find the Sum of the Interior Angles of a Polygon? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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Transversal

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How Do You Find Missing Angles in a Transversal Diagram? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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Why SSA doesn't work

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Congruent triangles - Why SSA does not work

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Why AAA doesn't work

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Congruent triangles - Why AAA does not work

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AAS

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Definition: Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

There are five ways to test that two triangles are congruent. This is one of them (AAS). For a list see Congruent Triangles. If there are two pairs of corresponding angles and a pair of corresponding opposite sides that are equal in measure, then the triangles are congruent.

By opposite side we mean a side opposite either one of the angles. Either one will do, but it has to be the same one in both triangles obviously. In the figure below we have chosen the side QR which is opposite the angle P.

Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to the triangle PQR.

Notice that the the two angles and the opposite side are drawn in thick blue lines to indicate they are the parts being used to test for congruence.
What does this mean?
Because the triangles are congruent:

1. the other two sides are equal (PQ=LM, and PR=LN)

2. the third angles a re equal (Q=M)

But don't forget:
Congruent triangles can be rotated and/or mirror images of each other (reflected). (SeeCongruent triangles.) In the figure above, the two triangles have all three corresponding sides equal in length and so are still congruent, even though one is the mirror image of the other and rotated.
Other congruence topics

Congruent Triangles

Congruent Polygons

(C) 2011 Copyright Math Open Reference.
All rights reserved

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AAS Congruent Triangles - Math Open Reference

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Definition: Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles. There are five ways to test that two triangles are congruent. This is one of them (AAS). For a list see Congruent Triangles.

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SAS

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Definition: Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.

There are five ways to test that two triangles are congruent. This is one of them (SAS). For a list see Congruent Triangles. If any two corresponding sides and their included angle are the same in both triangles, then the triangles are congruent.

Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to the triangle PQR.

Notice that the the two sides and included angle are drawn in thick blue lines to indicate they are the parts being used to test for congruence.
What does this mean?
Because the triangles are congruent:

1. the third sides are also equal (PQ = LM)

2. the remaining two correspnding angles are equal (P=L and Q=M)

But don't forget:
Congruent triangles can be rotated and/or mirror images of each other (reflected). (SeeCongruent triangles.) In the figure above, the two triangles have all three corresponding sides equal in length and so are still congruent, even though one is the mirror image of the other and rotated.
Other congruence topics

Congruent Triangles

Congruent Polygons

(C) 2011 Copyright Math Open Reference.
All rights reserved

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SAS Congruent Triangles - Math Open Reference

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Definition: Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles. There are five ways to test that two triangles are congruent. This is one of them (SAS). For a list see Congruent Triangles.

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ASA

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Definition: Triangles are congruent if any two angles and their included side are equal in both triangles.

There are five ways to test that two triangles are congruent. This is one of them (ASA). For a list see Congruent Triangles. If any two angles and the included side are the same in both triangles, then the triangles are congruent.

Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to the triangle PQR.

Notice that the the two angles and included side are drawn in thick blue lines to indicate they are the parts being used to test for congruence.
What does this mean?

1. Since two angles and the included side are equal in both triangles, we can be sure the triangles are congruent.

2. Because the triangles are congruent, the third angles (R and N) are also equal

3. Because the triangles are congruent, the remaining two sides are equal (PR=LN, and QR=MN)

But don't forget:
Congruent triangles can be rotated and/or mirror images of each other (reflected). (SeeCongruent triangles.) In the figure above, the two triangles have all three corresponding sides equal in length and so are still congruent, even though one is the mirror image of the other and rotated.
Other congruence topics

Congruent Triangles

Congruent Polygons

(C) 2011 Copyright Math Open Reference.
All rights reserved

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ASA Congruent Triangles - Math Open Reference

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Definition: Triangles are congruent if any two angles and their included side are equal in both triangles. There are five ways to test that two triangles are congruent. This is one of them (ASA). For a list see Congruent Triangles. If any two angles and the included side are the same in both triangles, then the triangles are congruent.

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SSS

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Definition: Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.

There are five ways to test that two triangles are congruent. This is one of them (SSS). For a list see Congruent Triangles. If all three sides in one triangle are the same length as the corresponding sides in the other, then the triangles are congruent.

Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to the triangle PQR.

Notice that the the three sides are drawn in thick blue lines to indicate they are the parts being used to test for congruence.
What does this mean?

1. Since all three corresponding sides are the same length, we can be sure the triangles are congruent.

2. Because the triangles are congruent, this means that the three angles at P,Q and R are equal to the angles L,M and N respectively.

But don't forget:
Congruent triangles can be rotated and/or mirror images of each other (reflected). (SeeCongruent triangles.) In the figure above, the two triangles have all three corresponding sides equal in length and so are still congruent, even though one is the mirror image of the other and rotated.
Other congruence topics

Congruent Triangles

Congruent Polygons

(C) 2011 Copyright Math Open Reference.
All rights reserved

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SSS Congruent Triangles - Math Open Reference

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Definition: Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other. There are five ways to test that two triangles are congruent. This is one of them (SSS). For a list see Congruent Triangles.

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How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.