Unit 8 Lesson 7" Proving Similar Triangles

Question 1

Angle-Angle Similarity Postulate

Answer 1

a hypothesis that states that two triangles are similar if two of their corresponding angles are congruent

Question 2

corresponding angles

Answer 2

angles that are formed by corresponding congruent sides

Question 3

similar triangles

Answer 3

triangles that have corresponding sides in the same ratio (or proportion) and congruent corresponding angles

Question 4

midsegment

Answer 4

a segment joining the midpoints of two sides of a triangle

Question 5

SAS Similarity Theorem

Answer 5

the theorem that states that if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar

Question 6

Triangle Midsegment Theorem

Answer 6

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Question 7

What is the strategy for proving the Triangle Midsegment Theorem?

Answer 7

First, prove that the smaller triangle created by the midsegment is similar to the original triangle and that the smaller triangle has sides that are half the length of the sides of the larger triangle. You can then show that the midsegment is half the length of the third side of the triangle. Because the triangles are similar, there are congruent corresponding angles. This implies that the midsegment and third side of the triangle must be parallel.

Question 8

congruence

Answer 8

a term used to describe having the same shape and size

Question 9

similarity

Answer 9

a number of figures that have the same shape but a different size; in geometry, all angles are congruent, but side lengths differ proportionally

Question 9

congruent

Answer 9

of the same shape and size; in geometry, congruent parts overlap perfectly when placed on top of one another