Proving Congruence by Side, Angle, Side I
H
Two triangles are congruent if two
GHKJ
11-/130°
GI EKL
11- 1300L
sides and the angle they form on
one triangle are congruent to two ZGZK
sides and the angle they form on A GHI = AJKL
the other triangle.
Use the Side, Angle, Side Rule (SAS) to prove that the triangles in each pair are
congruent. Draw hash marks to show the congruent sides and angles. Then write the
congruence statements for each pair of triangles.
1.
2.
3.
G
4
8
D
8
P
6
8/1000
3
6
8 /100°
3
blog
5
5
M
5
B
4
A
B
R
N
5.
6.
R
13
A
N
L
E
T
-В
7 1019
10197
6
3
6
7
509
650
8
D
N

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.