Chapter 13 (PDF)

2. Flowchart Proof
PQ ST PQR TSU QPR STU
Given
AIA Theorem Given
3. Flowchart Proof
ABC
Given
a b c 180°
Triangle Sum
Theorem
LESSON 13.3 • Triangle Proofs
Proofs may vary.
1. Flowchart Proof
XY ZY
Given
XZ WY
Given
WY WY
Reflexive
property
WXY WZY
SAS Theorem
QRP TUS
Third Angle
Theorem
PR UT
Converse of
AEA Theorem
a x
VA Theorem
x b c 180°
Substitution
x y c 180°
Substitution
x y z 180°
Substitution
XZY is isosceles
Definition of
isosceles triangle
YM is the altitude
from vertex Y
Definition of altitude
and vertex angle
YM is angle
bisector of XYZ
Isosceles Triangle
Vertex Angle Theorem
XYM ZYM
Definition of
angle bisector
b y
VA Theorem
c z
VA Theorem
2. Proof:
Statement Reason
1. CD BD 1. Given
2. BD AB 2. Given
3. CD AC 3. Given
4. AD is bisector 4. Converse of Angle
of CAB Bisector Theorem
5. CAD BAD 5. Definition of angle
bisector
6. ACD is a right 6. Definition of
angle perpendicular
7. ABD is a right 7. Definition of
angle perpendicular
8. ACD ABD 8. Right Angles Are
Congruent Theorem
9. ABD ACD 9. SAA Theorem
3. Flowchart Proof
MN QM
Given
QMN and NMO
are supplementary
Linear Pair Postulate
4. Proof:
MN NO
Transitivity
MNO is isosceles
Definition of
isosceles triangle
NMO NOP
IT Theorem
QMN RON
Supplements of
Congruent Angles
Theorem
Statement Reason
1. AB BC 1. Given
NO QM
Given
RON and NOP
are supplementary
Linear Pair Postulate
2. ABC is isosceles 2. Definition of isosceles
triangle
3. A ACB 3. IT Theorem
4. ACB DCE 4. Given
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