Proving Triangle Similarity

Front

What is triangle similarity?

Back

Triangle similarity means that two triangles have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What are the criteria for proving triangle similarity?

Back

The criteria for proving triangle similarity are: AA (Angle-Angle), SAS (Side-Angle-Side), and SSS (Side-Side-Side).

Front

Define AA similarity criterion.

Back

AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

Define SAS similarity criterion.

Back

SAS similarity criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

Define SSS similarity criterion.

Back

SSS similarity criterion states that if the three sides of one triangle are in proportion to the three sides of another triangle, then the triangles are similar.

Front

If triangle YXZ is similar to triangle AXB, what can be said about their angles?

Back

If triangle YXZ is similar to triangle AXB, then angle Y is equal to angle A, angle X is equal to angle B, and angle Z is equal to angle X.

Front

If Lance the alien is 5 feet tall and his shadow is 8 feet long, how do you find the height of a tree with a 32 feet shadow?

Back

Use the proportion of heights to shadows: (Height of Lance / Shadow of Lance) = (Height of Tree / Shadow of Tree). Thus, (5/8) = (Height of Tree / 32). Solving gives Height of Tree = 20 feet.

Front

What does it mean if two triangles are not similar?

Back

If two triangles are not similar, it means that their corresponding angles are not equal and/or their corresponding sides are not in proportion.

Front

What is the significance of the included angle in SAS similarity?

Back

The included angle in SAS similarity is crucial because it must be equal for the triangles to be considered similar.

Front

How can you determine if two triangles are similar using the SSS criterion?

Back

To determine if two triangles are similar using the SSS criterion, calculate the ratios of the lengths of corresponding sides. If all three ratios are equal, the triangles are similar.