Answer Key

Lesson 1.6

Study Guide

1. not a polygon

2. polygon; convex

3. not a polygon

4. polygon; concave

5. quadrilateral; regular

6. 16 mm

Answer Key

Lesson 8.1

Study Guide

1. 18008 2. pentagon 3. 71 4. 438

Answer Key

Lesson 8.2

Study Guide

1. x 5 5, y 5 14 2. a 5 10, b 5 5 3. p 5 33

4. m 5 13 5. 30.75 6. 8 7. 508 8. 1308

9. 1 2 3 } 2 ,

1 }

2 2 10. 1 2

1 } 2 , 3 2

Answer Key

Lesson 8.3

Study Guide

1. Theorem 8.10 2. Theorem 8.7

3. Theorem 8.8 4. Theorem 8.9 5. 1 }

2

6. LM 5 Ï}}}

(25 2 (24))2 1 (22 2 2)2 5 Ï}

17 ;

NO 5 Ï}}}

(0 2 (21))2 1 (0 2 (24))2 5 Ï}

17 ;

because LM 5 NO 5 Ï}

17 , } LM > }

NO .

Slope of } LM 5 22 2 2

} 25 2 (24)

5 4;

slope of }

NO 5 0 2 (24)

} 0 2 (21)

5 4; because } LM and }

NO

have the same slope, they are parallel.

} LM and }

NO are congruent and parallel. So, LMNO is a parallelogram by Theorem 8.9.

Answer Key

Lesson 8.4Study Guide

1. always

2. sometimes

3. always

4. The quadrilateral has four congruent sides, so it is a rhombus. Because all four angles are congruent, by the Corollary to Theorem 8.1, the measure of each angle is 3608 4 4 5 908, and the quadrilateral is a rect-angle. So, by the Square Corollary, the quadrilateral is a square.

5. The diagonals bisect each other, so by Theorem 8.10 the quadrilateral is a parallelogram. The diagonals are perpendicular, so by Theorem 8.11 the parallelogram is a rhombus.

6.

By definition, square ABCD is a parallelogram with four congruent sides and four right angles. Because ABCD is a parallelogram, it also has these properties: Opposite sides are parallel and congruent; opposite angles are congruent; consecutive angles are supplementary; and diagonals bisect each other. Because squares are also rectangles, by Theorem 8.12, the diagonals of ABCD are congruent.

Answer Key

Lesson 8.5

Study Guide

1. Slope of }

AB 5 2 1 } 2 ; slope of

} DC 5 0;

slope of }

AD 5 3; slope of }

BC 5 3; }

AD and }

BC have equal slopes, so they are parallel. }

AB and }

DC do not have equal slopes, so they are not parallel. Because ABCD has exactly one pair of parallel sides, it is a trapezoid. 2. 7 3. 9

4. 21; 1268

Answer Key

Lesson 8.6Study Guide

1. rectangle, square, isosceles trapezoid 2. kite

3. rhombus; Rhombus Corollary

4. rectangle; Corollary to Theorem 8.1 and Rectangle Corollary

5. isosceles trapezoid; definition of trapezoid and Theorem 8.15

6. Yes, because ∠ A and ∠ D are supplementary, }

AB i } CD , and because }

AB Þ }

CD , ABCD cannot be a paral-lelogram. So ABCD is a trapezoid.