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Triangle Similarity. Advanced Geometry Similarity Lesson 3. In the Triangle Congruence unit we talked about four tests for proving that two triangles are congruent ;. SSS Congruence, SAS Congruence, ASA Congruence, and AAS Congruence.

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Triangle similarity

Triangle Similarity

Advanced Geometry

Similarity

Lesson 3


In the Triangle Congruence unit we talked about four tests for proving that two triangles are congruent;

SSS Congruence,

SAS Congruence,

ASA Congruence, and

AAS Congruence.

There are also tests to prove that two TRIANGLES are similar:

AA Similarity,

SSS Similarity, and

SAS Similarity


AA Similarity

Two pairs of corresponding angles are CONGRUENT.


SSS Similarity

Three pairs of corresponding sides are PROPORTIONAL.


SAS Similarity

Two pairs of corresponding sides are PROPORTIONAL

and

the included angles are CONGRUENT.


EXAMPLES:

Determine whether each pair of triangles is similar.

Justify your answer.

Yes;

AA Similarity

No;

Correpsonding sides are not proportional.

No;

There is not enough information.


EXAMPLE:

Given

RS = 4, RQ = x + 3, QT = 2x + 10,

and UT = 10. Find RQ and QT.


EXAMPLE:

Josh wanted to measure the height of the Sears Tower

in Chicago. He used a 12-foot light pole and measured

its shadow at 1 p.m. The length of the shadow was 2 feet.

Then he measured the length of Sears Tower’s

shadow and it was 242 feet at the same time.

What is the height of the Sears Tower?


EXAMPLE:

Triangles KLJ and MNJ have vertices

Justify that


EXAMPLE:

Simplify


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