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
