CONGRUENT AND SIMILAR TRIANGLES. Congruency Two shapes are congruent if one of the shapes fits exactly on top of the other shape. In congruent shapes:

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Presentation transcript:

CONGRUENT AND SIMILAR TRIANGLES

Congruency Two shapes are congruent if one of the shapes fits exactly on top of the other shape. In congruent shapes: corresponding angles are equal corresponding lengths are equal These three triangles are all congruent

To prove that two triangles are congruent you must show that they satisfy one of the following four sets of conditions: ASA: two angles and the included side are the same SSS: three sides are equalSAS: two sides and the included angle are the same RHS: right-angled triangle with hypotenuse and one other side the same

A Which triangles are congruent to triangle A?

Similar shapes In similar shapes: corresponding angles are equal corresponding sides are in the same ratio These two quadrilaterals are similar. A B C D PQ R S To show that two triangles are similar it is sufficient to show that just one of the above conditions is satisfied.

Which triangles are similar to triangle A? A

The triangles are similar. Find the values of x and y. (All lengths are in cm.) Examples x y Using ratio of corresponding sides: Finding Missing Lengths in Similar Shapes

The triangles are similar. Find the values of x and y. (All lengths are in cm.) Examples 2 Using ratio of corresponding sides: 7 8 x y Turn one of the triangles so that you can see which are the corresponding sides. 7

3Find the values of x and y. (All lengths are in cm.) x 2.5 Examples 9 y 6 2 8x +2.5 y x 6 9 Using ratio of corresponding sides: Separate the two triangles.

Starter Page 127 Q5b Find x and y y x 18

4 Example x 9 x 4 6 y y Using ratio of corresponding sides: Find the values of x and y. (All lengths are in cm.) Turn the top triangle so that you can see which are the corresponding sides.

6 Question y 20 y 6 x x 12 Using ratio of corresponding sides: Find the values of x and y. (All lengths are in cm.) Turn the top triangle so that you can see which are the corresponding sides.

Page 126 Ex 3.11 Q1,2 and 9