Find sides and angles with congruent relationships

 

Congruent triangles are triangles that are identical in shape and size. In other words, all corresponding sides and angles are equal. 

So once we know that triangles are congruent, we can find any unknown side lengths or angles. We just need to find the corresponding value on the other triangle. We can do this because corresponding sides and angles are equal in congruent triangles.

This seems straight forward but sometimes triangles may be flipped or rotated so you just need to make sure you've got corresponding information. 

 

Examples

Question 1

Given that these shapes are congruent, find the values of $x$x and $y$y.

 

Think: We need to find which sides in the first triangle correspond to those in the second triangle. We can translate the shapes so they look identical to help us do this if needs be.

Do: The two single lines indicate that these sides are corresponding. So $x=6$x=6cm. Similarly, the other side we are trying to find is the hypotenuse of the right-angled triangle, so $y=15$y=15cm.

Question 2

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The two given triangles are congruent. By considering the relative position of angles and sides, or otherwise, find the missing values. Give a reason for each answer.

a) Solve for $x$x.

b) Solve for $y$y.

c) Solve for $z$z. 

 

Question 3

The given triangles are congruent.

a) Which of the given statements correctly show that the two triangles are congruent.

b) Which congruence test justifies their congruence?

c) Hence, find the value of the pronumeral.