Similarity Criteria, Proportions & Midsegments

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What does SSS stand for in similarity criteria?

Back

Side-Side-Side: If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

Front

What does SAS stand for in similarity criteria?

Back

Side-Angle-Side: If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does AA stand for in similarity criteria?

Back

Angle-Angle: If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the Midsegment Theorem?

Back

A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle. It is parallel to the third side and half its length.

Front

If the length of a midsegment is 6, what is the length of the third side?

Back

12 (since the midsegment is half the length of the third side).

Front

How do you find the missing length in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides of the similar triangles.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding sides?

Back

The lengths of corresponding sides are in proportion.

Front

What is the value of x if the sides of triangle ABC are 3, 4, and x, and the sides of triangle DEF are 6, 8, and 12?

Back

x = 6 (since the triangles are similar, the sides are proportional).