Download CCSS ARGUMENTS Write a two-column proof. 23. Given: bisects B

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Transcript 
4-3 Congruent Triangles
CCSS ARGUMENTS Write a two-column proof.
23. Given:
bisects B.
Prove: A C
SOLUTION: Proof:
Statements (Reasons)
1.
,
. (Given)
bisects 2.
(Def. of angle bisector)
3.
are right angles. ( lines form rt.
4.
are .)
(All rt. 5.
(Third Thm.)
24. Given:
P
T,
S
.)
Q
Prove:
SOLUTION: Proof:
Statements (Reasons)
1.
,
,
(Given)
(Symm. Prop.)
2.
3.
(Trans. Prop)
4.
(Symm. Prop.)
5.
6.
7.
(Trans. Prop.)
(Vert. are .)
s)
(Def. of ALGEBRA Draw and label a figure to represent the congruent triangles. Then find x and y.
, AB = 7, BC = 9, AC = 11 + x, DF = 3x – 13, and DE = 2y – 5
28. SOLUTION: eSolutions Manual - Powered by Cognero
Page 1
4.
(Symm. Prop.)
5.
(Trans. Prop.)
6.
(Vert. are .)
4-3 Congruent
Triangles
7.
s)
(Def. of ALGEBRA Draw and label a figure to represent the congruent triangles. Then find x and y.
, AB = 7, BC = 9, AC = 11 + x, DF = 3x – 13, and DE = 2y – 5
28. SOLUTION: Since the triangles are congruent, the corresponding sides are congruent.
Similarly, AB = DE.
That is, y = 6.
29. ,m
L = 49, m M = 10y, m
S = 70, and m
T = 4x + 9
SOLUTION: Since the triangles are congruent, the corresponding angles are congruent.
.
and By the definition of congruence
.
Substitute.
So,
.
Use the Triangle Angle Sum Theorem in
eSolutions Manual - Powered by Cognero
Page 2
.
4-3 Congruent
Triangles
That is, y = 6.
29. ,m
L = 49, m M = 10y, m
S = 70, and m
T = 4x + 9
SOLUTION: Since the triangles are congruent, the corresponding angles are congruent.
.
and By the definition of congruence
.
Substitute.
So,
.
Use the Triangle Angle Sum Theorem in
By the definition of congruence
Substitute.
.
.
That is,
30. , JK = 12, LJ = 5, PM = 2x – 3,
= 67,
= y + 4 and
= 2y – 15
SOLUTION: Since the triangles are congruent, the corresponding angles and corresponding sides are congruent.
eSolutions Manual - Powered by Cognero
Page 3
4-3 Congruent Triangles
That is,
30. , JK = 12, LJ = 5, PM = 2x – 3,
= 67,
= y + 4 and
= 2y – 15
SOLUTION: Since the triangles are congruent, the corresponding angles and corresponding sides are congruent.
39. CHALLENGE Find x and y if
.
SOLUTION: If two triangles are congruent, then their corresponding sides are congruent.
Substitute.
eSolutions Manual - Powered by Cognero
Substitute
in Page 4
4-3 Congruent Triangles
39. CHALLENGE Find x and y if
.
SOLUTION: If two triangles are congruent, then their corresponding sides are congruent.
Substitute.
Substitute
Substitute
in in eSolutions Manual - Powered by Cognero
Page 5
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