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NAME
DATE
6-4
PERIOD
Skills Practice
Rectangles
ALGEBRA Quadrilateral ABCD is a rectangle.
A
1. If AC = 2x + 13 and DB = 4x - 1, find DB. 27
E
D
B
C
2. If AC = x + 3 and DB = 3x - 19, find AC. 14
3. If AE = 3x + 3 and EC = 5x - 15, find AC. 60
4. If DE = 6x - 7 and AE = 4x + 9, find DB. 82
5. If m∠DAC = 2x + 4 and m∠BAC = 3x + 1, find m∠BAC. 52
6. If m∠BDC = 7x + 1 and m∠ADB = 9x - 7, find m∠BDC. 43
7. If m∠ABD = 7x - 31 and m∠CDB = 4x + 5, find m∠ABD. 53
8. If m∠BAC = x + 3 and m∠CAD = x + 15, find m∠BAC. 39
9. PROOF: Write a two-column proof.
3
4
Given: RSTV is a rectangle and U is the
−−
midpoint of VT.
Prove: RUV SUT
Statements
Reasons
1.
2.
3.
4.
5.
6.
7.
1.
2.
3.
4.
5.
6.
7.
RSTV is a rectangle.
∠V and ∠T are right angles.
∠V ∠T
−−
U is the midpoint of VT.
−− −−
VU TU
−− −−
VR TS
RUV SUT
7
6
5
Given
Definition of rectangle
All rt are .
Given
Definition of midpoint
Opp sides of are congruent.
SAS
COORDINATE GEOMETRY Graph each quadrilateral with the given vertices.
Determine whether the figure is a rectangle. Justify your answer using the
indicated formula.
See students’ graphs.
10. P(-3, -2), Q(-4, 2), R(2, 4), S(3, 0); Slope Formula
No; Sample answer: Angles are not right angles.
11. J(-6, 3), K(0, 6), L(2, 2), M(-4, -1); Distance Formula
Yes; Sample answer: Both pairs of opposite sides are congruent
and diagonals are congruent.
12. T(4, 1), U(3, -1), X(-3, 2), Y(-2, 4); Distance Formula
Yes; Sample answer: Both pairs of opposite sides are congruent and the
diagonals are congruent.
Chapter 6
25
Glencoe Geometry
Lesson 6-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Proof