Core Connections Geometry, 2013
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Core Connections Geometry, 2013 View details
1. Section 7.1
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Exercise 6 Page 400

a We are given two triangles and want to justify the relationship between them. In both triangles we know two angles. We have also been given two sides in and one side in
If two triangles have at least two pairs of congruent angles, they are similar. Using the Triangle Angle Sum Theorem, we can find the measure of
We can use the Triangle Angle Sum Theorem again to find the measure of
As we can see, and have two pairs of congruent angles, and and and Therefore, the triangles are similar by the AA (Angle-Angle) Similarity Theorem. To determine if the triangles are congruent, we must identify pairs of corresponding sides of the two triangles.

From the diagram we see that two pairs of corresponding angles — and and and — and the side between them are congruent. Therefore, we can claim that the triangles are congruent by the ASA (Angle-Side-Angle) Congruence Theorem. Let's show this as a flowchart.

b From Part A, we know that the triangles are congruent. This means corresponding sides have equal measures.
We know that and since we can claim that as well. Finally, to find we can use the Law of Sines.
Solve for