Page 82 - Math Course 3 (Book 2)

Congruent Triangles

Let’s Begin

Corresponding Congruent Parts

Example

ARCHITECTURE
A tower’s roof is composed of congruent triangles
all converging toward a point at the top. Name the
corresponding congruent angles and sides of
△HIJ and △LIK.
I

Use the Distance Formula to find the length of
each side of the triangles.

H L RS = (–3 – 0)² + (0 – 5)²
J K
= 9 + 25 or 34

R’S’ = (3 – 0)² + (0 – (–5))²
Since corresponding parts of
congruent triangle are congruent, = 9 + 25 or 34
Answer ∠HJI ≅ ∠KLI, ∠JHI ≅ ∠LKI,
∠HIJ ≅ ∠KIL, HI ≅ LI, HJ ≅ LK, and
JI ≅ KI. ST = (0 – 1)² + (5 – 1)²

= 1 + 16 or 17
A tower’s roof is composed of congruent triangles
all converging toward a point at the top. Name the S’T’ = (0 – (–1))² + (–5 –(–1))²
congruent triangles.
= 1 + 16 or 17
Answer ΔHIJ ≅ ΔKIL
TR = (1 – (–3))² + (1 – 0)²

Transformations in the Coordinate Plane = 16 + 1 or 17

Example T’R’ = (–1 –3)² + (–1 – 0)²
= 16 + 1 or 17
COORDINATE GEOMETRY
The vertices of ΔRST are R(–3, 0), S(0, 5), and The lengths of the corresponding
T(1, 1). The vertices of ΔR’S’T’ are R’(3, 0), Answer sides of two triangles are equal.
S’(0, –5), and T’(–1, –1). Verify that Therefore, by the definition of
34
ΔRST ≅ ΔR’S'T’. congruence, RS = R’S’ = ,
ST = S’T’ = TR = T’R’ = .
17
17
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