Answer Key
Lesson 8.2
Challenge Practice
1. (21, 5), (7, 5)
2. (2, 1), (2, 3)
3. (a 1 2, b 1 3), (a 1 6, b 1 3)
4.
(
a2, b2
)
,
(
a 1 a2, b2
)
5. 2
6. All four vertices of a parallelogram can only have at most two equal x-values and two equal y-values.
So the third and fourth vertices of the parallelogram cannot have the same x-values or y-values as the other
vertices if there are already two equal x-values or two equal y-values.
7. Sample answer: Draw the diagonal of one vertex to the opposite vertex to create two congruent trian-
gles. This can be done in two ways.
8. Sample answer: Draw a diagonal connecting two opposite vertices and then draw another diagonal
connecting the other two opposite vertices.
9. Sample answer: First Way: Connect one vertex to the midpoint of the opposite side. Repeat for the op-
posite vertex. Next draw the diagonal connecting the remaining opposite vertices. Second Way: Repeat the
first method but connect the other opposite vertices with a diagonal.
10. No.
11. Sample answer:
Statements Reasons
1. RSTU and WXYZ are 1. Given
parallelograms.
2.
}
RS i
}
UT ,
}
RU i
}
ST , 2. Definition of a
}
WX i
}
ZY , and parallelogram
}
WZ i
}
XY
3. ∠ RWX > ∠ YXW 3. Alternate Interior Angles Theorem
4. ∠ YXW > ∠ WZY 4. Opposite angles of a parallelogram are congruent.
5. ∠ WZY > ∠ TYZ 5. Alternate Interior Angles Theorem
6. ∠ RWX > ∠ TYZ 6. Substitution Prop. of Equality
7. ∠ XRW > ∠ UZR 7. Alternate Interior Angles Theorem
8. ∠ SXT > ∠ YTZ 8. Alternate Interior Angles Theorem
9. ∠ XRW > ∠ SXT 9. Corresponding Angles Postulate
10. ∠ XRW > ∠ YTZ 10. Substitution Prop. of Equality
11. n RWX , n TYZ 11. Angle-Angle Similarity Post.
12.
Given: WXYZ is a parallelogram and
}
WY and
}
XZ are diagonals of WXYZ.
Prove: D is the midpoint of the segment with endpoints on opposite sides passing through the point of inter-
section D.
