Pre-AICE 2: Unit 5 Exam - Study Guide

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Pre-AICE 2: Unit 5 Exam - Study Guide 1 Find the value of x. (The figure may not be drawn to scale.) A. 74 B. 108 C. 49 D. 51 2 Find the measure of an interior angle and an exterior angle of a regular polygon with 20 sides. 3 Consecutive angles in a parallelogram are always. A. congruent angles B. complementary angles C. supplementary angles D. vertical angles 4 Find the value of the variables in the parallelogram. F. x = 52, y = 10.5, z = 159 G. x = 21, y = 55, z = 104 H. x = 55, y = 21, z = 104 I. x = 10.5, y = 52, z = 159 Use the diagram to find the given length.

5 AC 6 BD 7 Complete the steps of this proof. Given: parallelogram WXYZ Prove: 8 Given the following, determine whether quadrilateral XYZW must be a parallelogram. Justify your answer.. X Y N W Z 9 Which statement is true? A. All quadrilaterals are squares. B. All rectangles are squares.

C. All parallelograms are quadrilaterals. D. All quadrilaterals are parallelograms. 10 If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure? 11 If the diagonals of a parallelogram are equal in length, then the parallelogram is also what type of figure? 12 Quadrilateral DEFG is a rhombus. What is the value of x? You can use the following fact to help you: If two sides of a triangle are congruent, then the angles opposite them are congruent. (The figure may not be drawn to scale.) 13 Writing: Explain the difference between a rhombus and a rectangle. 14 Isosceles trapezoid JKLM has legs and, and base If and find the value of x. F. 1 H. 19 G. 11 I. 8 2 3 15 Choose the statement that is NOT always true. For an isosceles trapezoid. A. the diagonals are congruent B. the base angles are congruent C. the diagonals are perpendicular D. the legs are congruent 16 Given: Trapezoid ABCD with midsegment. If and, find the length of. 17 SHORT RESPONSE Write your answer on a separate piece of paper. Figure ABCD below is a trapezoid.

Find the value of a, and then describe two ways to find the value of c and give its value. 18 The coordinates of quadrilateral PQRS are P( 3, 0), Q(0, 4), R(4, 1), and S(1, 3). What best describes the quadrilateral? F. a rectangle G. a square H. a rhombus I. a parallelogram What name best describes the quadrilateral? 19 A. parallelogram B. rhombus C. kite D. rectangle 20 F. kite G. rectangle H. parallelogram I. triangle 21 Describe the figure using as many of these words as possible: rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus.

22 Find the value of x. The diagram is not to scale. (2x + 10)º 148º (2x)º 112º F. 90 G. 35 H. 100 I. 45 23 This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. x x A. 18 B. 54 C. 36 D. 72 24 For the parallelogram, if and find The diagram is not to scale. 3 4 2 1 F. 9 G. 17 H. 173 I. 163

25 Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. A B 4x 2 y + 14 4y 7 x + 28 D C A. x = 10, y = 38 B. x = 10, y = 21 C. x = 10, y = 7 D. x = 7, y = 10 26 What is the value of x? A B L M D C F. 33 G. 29 H. 238 I. 37 27 Find in the kite. The diagram is not to scale. A D 3 39 1 2 B C A. 51, 51 B. 39, 39 C. 39, 51 D. 51, 39 28 Find the values of the variables and the lengths of the sides of this kite.

y 4 x + 5 2x + 5 x + 12 F. x = 7, y = 16; 3, 21 H. x = 7, y = 16; 12, 19 G. x = 16, y = 7; 12, 12 I. x = 16, y = 7; 3, 21 29 For what values of x and y must this quadrilateral be a parallelogram? Find the lengths of the sides. The diagram is not to scale. 4x 2x + 4 6y 3y + 19

Pre-AICE 2: Unit 5 Exam - Study Guide Answer Section 1 ANS: D PTS: 1 DIF: 2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: exterior angle measures of polygons 2 ANS: MSC: Application PTS: 1 DIF: 2 STA: MA.912.G.2.2 TOP: Lesson 8.1 Find Angle Measures in Polygons KEY: regular polygon interior angle measures of polygons exterior angle measures of polygons MSC: Application 3 ANS: C PTS: 1 DIF: 1 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: parallelogram consecutive interior angles property MSC: Comprehension 4 ANS: G PTS: 1 DIF: 2 STA: MA.912.G.2.2 MA.912.G.4.6 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: angle measure parallelogram diagonals MSC: Application 5 ANS: 10 PTS: 1 DIF: 2 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: Parallelogram bisect diagonal MSC: Knowledge 6 ANS: 8 PTS: 1 DIF: 2 TOP: Lesson 8.2 Use Properties of Parallelograms KEY: Parallelogram bisect diagonal MSC: Knowledge 7 ANS: PTS: 1 DIF: 2 STA: MA.912.G.3.4

TOP: Lesson 8.2 Use Properties of Parallelograms KEY: MSC: Analysis 8 ANS: triangle parallelogram proof PTS: 1 DIF: 2 STA: MA.912.G.3.4 TOP: Lesson 8.3 Show that a Quadrilateral is a Parallelogram KEY: parallelogram quadrilateral justify diagonals MSC: Application 9 ANS: C PTS: 1 DIF: 1 STA: MA.912.G.3.2 MA.912.G.3.1 TOP: Lesson 8.4 Properties of Rhombuses, Rectangles, and Squares KEY: property quadrilateral geometric figure MSC: Knowledge 10 ANS: A rhombus PTS: 1 DIF: 1 STA: MA.912.G.3.2 TOP: Lesson 8.4 Properties of Rhombuses, Rectangles, and Squares KEY: perpendicular parallelogram rhombus diagonal MSC: Knowledge 11 ANS: A rectangle PTS: 1 DIF: 1 TOP: Lesson 8.4 Properties of Rhombuses, Rectangles, and Squares KEY: rectangle parallelogram diagonal MSC: Knowledge 12 ANS: PTS: 1 DIF: 2 STA: MA.912.G.2.2 TOP: Lesson 8.4 Properties of Rhombuses, Rectangles, and Squares KEY: solve angle rhombus MSC: Application 13 ANS: Sample answer: A rhombus is a quadrilateral with four congruent sides while a rectangle is a quadrilateral with four right angles. PTS: 1 DIF: 2 STA: MA.912.G.3.2 TOP: Lesson 8.4 Properties of Rhombuses, Rectangles, and Squares KEY: rectangle rhombus quadrilateral MSC: Comprehension 14 ANS: G PTS: 1 DIF: 3 STA: MA.912.G.2.5 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: isosceles trapezoid leg MSC: Application 15 ANS: C PTS: 1 DIF: 2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: property isosceles trapezoid MSC: Comprehension 16 ANS: 20

PTS: 1 DIF: 2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: midsegment trapezoid MSC: Application 17 ANS: The value of a is 119. The value of c can be found from the fact that sides and are parallel. That means that c + = 180, so Another way to find the value of c is to use the fact that the vertex angles of the trapezoid must total 360 : so PTS: 1 DIF: 2 STA: MA.912.G.2.2 TOP: Lesson 8.5 Use Properties of Trapezoids and Kites KEY: angle measure trapezoid MSC: Analysis 18 ANS: G PTS: 1 DIF: 2 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: coordinate geometry quadrilateral MSC: Comprehension 19 ANS: A PTS: 1 DIF: 1 STA: MA.912.G.3.1 MA.912.G.3.2 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: quadrilateral identify MSC: Knowledge 20 ANS: F PTS: 1 DIF: 1 STA: MA.912.G.3.1 MA.912.G.3.2 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: quadrilateral identify MSC: Knowledge 21 ANS: trapezoid, quadrilateral PTS: 1 DIF: 1 STA: MA.912.G.3.1 MA.912.G.3.2 TOP: Lesson 8.6 Identify Special Quadrilaterals KEY: square rectangle parallelogram rhombus trapezoid quadrilateral MSC: Knowledge 22 ANS: I PTS: 1 DIF: L4 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: 6-1.1 Find the sum of the measures of the interior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 3 Using the Polygon Angle-Sum Theorem KEY: Polygon Angle-Sum Theorem 23 ANS: C PTS: 1 DIF: L4 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: 6-1.2 Find the sum of the measures of the exterior angles of a polygon STA: MA.912.G.2.1 MA.912.G.2.2 TOP: 6-1 Problem 4 Finding an Exterior Angle Measure KEY: angle pentagon Polygon Angle-Sum Theorem 24 ANS: I PTS: 1 DIF: L4 REF: 6-2 Properties of Parallelograms OBJ: 6-2.1 Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G.4.5 TOP: 6-2 Problem 1 Using Consecutive Angles KEY: algebra parallelogram opposite angles consecutive angles 25 ANS: C PTS: 1 DIF: L3 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: 6-3.1 Determine whether a quadrilateral is a parallelogram STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 TOP: 6-3 Problem 1 Finding Values for Parallelograms KEY: algebra parallelogram diagonal

26 ANS: G PTS: 1 DIF: L3 REF: 6-6 Trapezoids and Kites OBJ: 6-6.1 Verify and use properties of trapezoids and kites STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 TOP: 6-6 Problem 3 Using the Midsegment of a Trapezoid KEY: trapezoid base angles 27 ANS: C PTS: 1 DIF: L3 REF: 6-6 Trapezoids and Kites OBJ: 6-6.1 Verify and use properties of trapezoids and kites STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 TOP: 6-6 Problem 4 Finding Angle Measures in Kites KEY: kite diagonal 28 ANS: H PTS: 1 DIF: L4 REF: 6-6 Trapezoids and Kites OBJ: 6-6.1 Verify and use properties of trapezoids and kites STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 TOP: 6-6 Problem 4 Finding Angle Measures in Kites 29 ANS: x = 7, y = 3; 18, 28 KEY: algebra kite PTS: 1 DIF: L4 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: 6-3.1 Determine whether a quadrilateral is a parallelogram STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 TOP: 6-3 Problem 1 Finding Values for Parallelograms KEY: algebra rectangle

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