Corresponding sides of the congruent figures are congruent.
A
m∠ NML=66^(∘)
B
KJ=15 inches
Practice makes perfect
We are given the figure of an umbrella.
In this umbrella, the triangle JLK is congruent to triangle NLM. We want to find the measure of angle NML if the measure of angle JKL is 66^(∘). Let's show the angles in the diagram.
Let's recall the definition of congruent figures.
Congruent Figures
Two figures are congruent figures if there is a transformation or sequence of transformations that maps one of the figures onto the other. Congruent figures have the same size and shape.
By the definition, since the congruent figures have the same size and shape, their corresponding angles are congruent angles. Let's write the corresponding congruent angles.
△ JLK ≅ △ NLM [0.5em]
∠ JLK ≅ ∠ NLM
∠ KJL≅ ∠ MNL
∠ JLK ≅ ∠ NML
From here we know that ∠ JKL is congruent with ∠ NML, so their measures are congruent. Since the measure of ∠ JKL is given as 66^(∘), the measure of ∠ NML is also 66^(∘).
Here we will find the length of KJ when the length of MN is 15 inches.
Let's use the property of congruent figures again — Corresponding sides of the congruent figures are congruent. Let's write the corresponding congruent sides.
△ JLK ≅ △ NLM [0.5em]
JL ≅ NL
JK≅ NM
LK ≅ LM
Since JK and MN are congruent, and since the length of MN is 15 inches, the length of JK is 15 inches.
