7.4 Start Thinking. 7.4 Warm Up. 7.4 Cumulative Review Warm Up
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1 7. Start Thinking rhombus and a square are both quadrilaterals with four congruent sides, but a square alwas contains four right angles. Examine the diagrams below and determine some other distinctive characteristics of the rhombus and the square. 5 5 x x 7. Warm Up Use the diagrams to determine the measure of each angle m 1. m 3. m 3. m 5. m 5 6. m umulative Review Warm Up etermine whether the statement is alwas, sometimes, or never true. Explain our reasoning. 1. n isosceles triangle is a right triangle.. right triangle is a scalene triangle. 3. n equilateral triangle is an equiangular triangle.. right triangle is an equilateral triangle. 6 Geometr opright ig Ideas Learning, LL Resources b hapter
2 Name ate 7. Practice In Exercises 1 5, the diagonals of rhombus intersect at E. Given that m E = 67, E = 5, and E = 1, find the indicated measure. 1. m E. m E 3. m E 5 E 1. E 5. E 67 In Exercises 6 and 7, find the lengths of the diagonals of rectangle JKL. 6. JL = 3x + K = x 1 7. JL = x 6 K = 3 x + 1 In Exercises 8 and 9, decide whether quadrilateral WXYZ is a rectangle, a rhombus, or a square. Give all names that appl. Explain our reasoning. 8. W( 3, 1, ) X( 3,, ) Y( 5,, ) Z( 5, 1) 9. W(, 1 ), X( 1, ), Y(, 1 ), Z( 1, ) 10. Use the figure to write a two-column proof. Given: PSUR is a rectangle. PQ TU P Q R Prove: QS RT S T U 11. In the figure, all sides are congruent and all angles are right angles. a. etermine whether the quadrilateral is a rectangle. Explain our reasoning. b. etermine whether the quadrilateral is a rhombus. Explain our reasoning. c. etermine whether the quadrilateral is a square. Explain our reasoning. E d. Find m E. e. Find m E. opright ig Ideas Learning, LL Geometr Resources b hapter 7
3 Name ate 7. Practice In Exercises 1 and, decide whether quadrilateral JKL is a rectangle, a rhombus, or a square. Give all names that appl. Explain our reasoning. 1. J( 3, 5, ) K( 7, 6, ) L( 6,, ) (, 1). J(, 1 ), K( 1, 5 ), L( 5, ), (, ) In Exercises 3 7, the diagonals of rhombus intersect at. Given that m = 53, = 16, and = 1, find the indicated measure. 3. m. m 5. m Find the point of intersection of the diagonals of the rhombus with vertices 1,, 3,, 5, 8, and 1, 6. ( ) ( ) ( ) ( ) 9. Use the figure to write a two-column proof. Given: WXYZ is a parallelogram. XWY XYW Prove: WXYZ is a rhombus. X Y W Z 10. Your friend claims that ou can transform ever rhombus into a square using a similarit transformation. Is our friend correct? Explain our reasoning. 11. quadrilateral has four congruent angles. Is the quadrilateral a parallelogram? Explain our reasoning. 1. quadrilateral has two consecutive right angles. If the quadrilateral is not a rectangle, can it still be a parallelogram? Explain our reasoning. 13. Will a diagonal of a rectangle ever divide the rectangle into two isosceles triangles? Explain our reasoning. 8 Geometr opright ig Ideas Learning, LL Resources b hapter
4 Name ate 7. Enrichment and Extension Properties of Special Parallelograms In Exercises 1 3, determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain. 1. The diagonals are congruent, but the quadrilateral has no right angles.. Each diagonal is 3 centimeters long and the two opposite sides are centimeters long. 3. Two opposite angles are right angles, but the quadrilateral is not a rectangle. In Exercises 7, use the information given in the diagram to solve for the missing variable.. Find the value of w. Q 7w Find the value of x. 6. Find the value of. L R 31z x N 7. Find the value of z. 9w 1 S 5z P 8. In LNP shown at the right, ( m LN m NLP x ) = 3, =, m NP = 1 x, and NP is an acute angle. Find m NLP. N L P 9. Write a coordinate proof of part of Theorem 7.13 (Hint: write the vertices in terms of a and b.) Given: FGH is a parallelogram. G HF Prove: FGH is a rectangle. H(?,?) (a,?) F(b, 0) G(?,?) opright ig Ideas Learning, LL Geometr Resources b hapter 9
5 Name ate 7. Puzzle Time What o You Have To Know To Get Top Grades In Geometr? Write the letter of each answer in the box containing the exercise number. omplete the sentence. 1. rhombus is a parallelogram with congruent sides.. rectangle is a parallelogram with four angles. 3. square is a with four congruent sides and four right angles.. parallelogram is a rhombus if and onl if its are perpendicular. 5. parallelogram is a rhombus if and onl if each diagonal a pair of opposite angles. 6. parallelogram is a rectangle if and onl if its diagonals are. ecide whether each is a rhombus, rectangle, square, none of these, or all of these. 7. ( 8, 3, ) ( 5, 3, ) ( 1, 0, ) (, 6) 8. ( 6, 3 ), ( 6, 8 ), (, 5 ), (, 0) 9. ( 7, 1), (, ), (, ), ( 3, ) nswers E. 61 H. diagonals G. two. four. square T. kite L. parallelogram T. none N. 111 O. acute L. right. intersects G. rhombus R. rectangle L. bisects. all E. 6 S. congruent O. angles P. 119 I. 5 U. 11 R. perpendicular Given rhombus, find the measure of the indicated angle in degrees. 10. m = 119. Find m. Find the length of the diagonals of rectangle QRST given the following information. 11. QS = x + 6, RT = 6x 1. QS = 9x + 1, RT = 11x Geometr opright ig Ideas Learning, LL Resources b hapter
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