Geometry Unit 2 Extra Review 1) If QRS TMV, name all of the corresponding sides and angles. Then, write a congruence statement using a different order than the given congruence statement. △ ≅ △ 2) Polygon ABCD polygon PQRS. Find the values of x and y. ≅ 3) Given the figures below, which theorem or postulate can be used to prove the two triangles are congruent to each other? a) b) c) d) 32 32 4) What value of x will prove that Triangle EAY is a right triangle? E 51 ° ° Y (2x + 6) ° (x - 3) A 5) Dylan’s house is 6 miles from school and 7 miles from the library. Dylan’s house, the school, and the library form a triangle. Find the range of values that the school is from the library. 6) Use the diagrams below to determine the relationship between the given angles or sides. Fill in with <, >, or =. a) mÐ1 _____ mÐ2 b) MS _____ LS c) mÐ1 _____ mÐ2 M I 2 __ 1 2 7 T 95° 8 99° S 1 __ I 7 6 L 7) Name the point of intersection of: a) Perpendicular Bisectors b) Angle Bisectors c) Medians d) Altitudes 8) Draw each type of triangle with the appropriate markings: a) Obtuse Scalene b) Acute Isosceles c) Equiangular 9) List the sides and angles in order from smallest to biggest a) b) B 28º L A 9 20 100º M 18 N C 10) Write an expression to represent the perimeter of the figure below. 11) Trapezoid LMNO is shown below. What must be the value of x to prove the trapezoid is an isosceles trapezoid? o (3x + 40) (6x + 10)o (5x + 60)o (10x + 10)o 12) The figure below is a rhombus. a) Which property explains why ? 푁푆���� ⊥ 푀푃����� b) Which property explains why ? ∡푁푃푀 ≅ ∡푆푃푀 c) Which property explains why ? 13) List all of the properties of a parallelogram (without looking at your notes). ∡푁푃푆 ≅ ∡푆푀푁 14) Julian claims that all quadrilaterals are parallelograms. Which statement below disproves Julian’s claim? A) A rectangle is a quadrilateral B) Quadrilaterals have four sides C) A rhombus is a quadrilateral D) A kite is a quadrilateral 15) An isosceles trapezoid has all properties of a trapezoid, has base angles congruent, and has legs congruent. What else is true about an isosceles trapezoid? 16) Determine whether the following are sometimes (S), always (A), or never (N) true. a) A parallelogram is a rectangle. b) A square is a rhombus. c) A kite is an isosceles trapezoid. d) An isosceles trapezoid has two congruent legs. e) A trapezoid has two pairs of opposite sides parallel. f) A kite has exactly one pair of opposite angles congruent. g) A square has congruent diagonals. h) The interior angles of a quadrilateral add up to 360°. 17) In the figure below: a) What is the relationship between the opposite angles? Explain how you know. b) What is the relationship between the consecutive angles? Explain how you know. c) What is the relationship between the diagonals? Explain how you know. 18) List all the quadrilaterals with: a) Both pairs of opposite sides congruent b) Diagonals that bisect each other c) Diagonals that are congruent d) Diagonals that are perpendicular to each other e) Exactly one pair of opposite angles congruent 19) Given quadrilateral PQRS with vertices P(5, 4), Q(3, -6), R(0, -10), and S(2, 0), find the lengths of the diagonals. 20) What type of quadrilateral is PQRS if the coordinates of the vertices are P(1, 1), Q(5, 3), R(7, 7), and S(3, 5)? 21) If quadrilateral PQRS is a kite with vertices Q(-2, 3), R(3, 6), and S(0, 1), what are the coordinates of the missing vertex P if the x-coordinate of P is -2? 22) Write an expression to represent the missing x-coordinate. 23) In the diagram, ∆EFG ≅ ∆HIJ. What is the measure of ? F I ∡퐻 o 65 35o E G J H 24) In the following figure, corresponds to which angle in ∆VUS? S U ∡푁 V A N 25) Given , what is the reason that + + = 180°? a) alternate∆ interior퐴퐵퐶 angles ∠퐴 ∠퐵 ∠퐶 b) corresponding angles c) the sum of the measures of the interior angles in a triangle is 180° d) definition of supplementary e) definition of complementary 26) Given rectangle WXYZ with diagonals that intersect at point R, which of the following must be true? Choose all that apply. a) b) c) d) 27)�푊푋�� �Which�� ≅ 푋푌��� �of the following푊푋����� ⊥is 푋푌�NOT��� a correct푊푅�� �ways�� ≅ 푋푅�to��� prove triangles푊푌����� ≅are푋푍�� �congruent?� Circle all that apply. a) 3 pairs of corresponding congruent sides b) 3 pairs of corresponding congruent angles c) 2 pairs of adjacent congruent sides and a the included angles are congruent d) 2 pairs of adjacent congruent angles and the included sides are congruent 28) What 2 reasons for proving triangles are congruent are missing from question 27? .