Int. Geometry Unit 7 Test Review 1

Transcription

1 Int. Geometry Unit 7 est eview uestions -0: omplete each statement with sometimes, always, or never.. he diagonals of a trapezoid are congruent.. rhombus is equiangular.. rectangle is a square.. he opposite angles of an isosceles trapezoid are congruent. 5. he diagonals of a square are perpendicular bisectors of each other. 6. he diagonals of a rhombus bisect each other. 7. rhombus is a rectangle. 8. he diagonals of a parallelogram bisect the angles of the parallelogram. 9. If the diagonals of a quadrilateral are perpendicular, then the quadrilateral is a rhombus. 0. quadrilateral with one pair of congruent sides and one pair of parallel sides is a parallelogram. irections -0: (a) Give the most accurate name for the quadrilateral (b) Write the reason why you may write a phrase or the entire theorem or definition that justifies your answer.. ; =. ; =. ; m = m m = m. m = m 5; =

2 Int. Geometry Unit 7 est eview 5. m = m = m 5= m 6 6. = = = m 7= m 8= m = m 7. ; = ; m + m = ; ; 9. = = = 0.. he angles of a pentagon are in the ratio (:5::6:5). What is the measure of the largest angle?. Find VW and VX given that U is a trapezoid. egment VW is a median. U V X Y W 8

3 Int. Geometry Unit 7 est eview. In isosceles trapezoid, m x and m in the following cases: a) b) = and m ( x 5) =. Find m. ne of the angles of a rhombus is 0. If the shorter diagonal is, what is the length of the longer diagonal? 5. uadrilateral WXYZ is a parallelogram. Given that WX = x, XY = x + 7, and YZ = x 8. What is the perimeter of WXYZ? 6. rapezoid is divided into four congruent trapezoids as shown. Given = and = 8, find the sum of all line segments in the figure. 7. If the degree measures of the angles of a hexagon are (x+0), (7x+0), 9x, 00 o, 80 o and 0x, what is the sum of the smallest angle and the largest angle? 8. diagonal of a rectangle forms a 0 with each of the longer sides of the rectangle. If the length of the shorter side is, what is the length of the diagonal? 9. If figure is a parallelogram, what is the value of y? x x y

4 Int. Geometry Unit 7 est eview 0. is a square and is an equilateral triangle. What is m?. regular pentagon and a regular octagon share a common side. side of each figure is extended to form a quadrilateral. What is the value of x? x. he measure of each exterior angle of a regular polygon is 0. ame the polygon.. he measure of each interior angle of a regular polygon is 6. ame the polygon.. Is it possible for a regular polygon to have an interior angle of 77.5 o? If so how many sides does the polygon have? 5. Given: ectangle and parallelogram E rove: Δ E is isosceles E

5 Int. Geometry Unit 7 est eview 5 6. Given: parallelogram ; E=F E rove: FE is a parallelogram F 7. Given: parallelogram E; E rove: is an isosceles trapezoid. E 8. Given: parallelogram ; = rove: = 9. Given: V; V; rove: and are complementary E V 0. Given: parallelogram ZY; ZY X; rove: ZY is a rhombus X Z Y

6 Int. Geometry Unit 7 est eview 6. Given: ZY; Y X rove: and X Z Y nswers:. omtimes. ometimes. ometimes. ever 5. lways 6. lways 7. ometimes 8. ometimes 9. ometimes 0. ometimes. arallelogram; one pair of congruent and parallel opposite sides. Kite; one diagonals are perpendicular and only one is bisected. arallelogram; opposite angles are congruent. Isosceles rapezoid; one pair of parallel sides (I theorem) and diagonals are congruent 5. hombus; parallelogram with diagonals that bisect the angles 6. ectangle; the diagonals bisect each other and diagonals are congruent 7. ectangle; it is a parallelogram (see # for reason) with one right angle 8. hombus; parallelogram (opposite sides are congruent) with perpendicular diagonals 9. hombus; congruent sides 0. rapezoid; one pair of parallel sides. 50 :. VW = 0; VX =. a) m = m = 5 b) m = 05 ; m = gon. 0-gon. Yes, -gon

7 Int. Geometry Unit 7 est eview 7 ote with the proofs, there are multiple solutions to these problems. 5. tatement eason. is a rectangle. Given. =. iagonals of a rect. are congruent. E is a parallelogram. Given. E=. pp. sides of a parallelogram are congruent 5. E= 5. ransitivity 6. Δ E is isosceles 6. efinition of Isos. riangle 6. tatement eason. is a parallelogram. Given. = and =. diagonals of a parallelogram bisect each other. E + E = and F + F =. egment ddition ost.. E+E=F+F. substitution 5. E = F 5. Given 6. E = EF 6. ubtraction oe 7. is the midpoint of EF 7. efinition of midpoint 8. is the midpoint of 8. efinition of a midpoint (see step ) 9. FE is a parallelogram 9. diagonals bisect each other (steps 8 and 9) 7. tatement eason. E is a parallelogram. Given. = E. opp. sides of a parallelogram are congruent. E. Given. E=. Isosceles riangle heorem 5. = 5. ransitivity 6. E 6. efinition of a parallelogram (step ) 7. is an isosceles trapezoid 7. efinition of an isos. rapezoid. 8. tatement eason. is a parallelogram. Given. = and. opposite sides and angles of a paralleogram are congruent. =. Given. Δ Δ. 5. = 5. efinition of congruent triangles

8 Int. Geometry Unit 7 est eview 8 9. tatement eason. V and V. Given. V is a parallelogram. efinition of a parallelogram.. Given. V is a rhombus. a parallelogram which has consecutive congruent sides is a rhombus 5. EV or m = m EV 5. In a rhombus the diagonals bisect the angles 6. V 6. diagonals of a rhombus are also perp. 7. EV is a right angle 7. efinition of perpendicular lines 8. Δ EV is a right triangle 8. ef of a right triangle (one right angle) 9. and EV are complementary 9. the acute angles of a right triangle are complementary 0. m + m EV = efinition of complementary angles. m + m = 90. ubstitution (step 5). and are complementary. efinition of omplementary ngles 0. tatement eason.. Given. X Z. Isosceles riangle heorem. ZY X. Given. ZY Z. ransitivity 5. parallelogram ZY 5. Given 6. ZY is a rhombus 6. parallelogram with two pair of consecutive congruent sides is a rhombus. tatement eason. ZY is a parallelogram. Given. Z=Y and Z Y. opposite sides are parallel and congruent.. orresponding ngle ost. Y=X. Given 5. X=Z 5. ransitivity Isosceles triangle theorem