End-of-Course Assessment

Name End-of-Course Assessment 1. Line GH is tangent to ⊙T ⏜ at N. If m∠ANG = 54°, what is mAB? ​​ 4. A rhombus has side lengths of 25. What could be the lengths of the diagonals? ​​ B 𝖠 22 and 40 𝖡 26 and 36 A T G N 𝖢 𝖣 26 and 48 30 and 40 5. What proportion could you use to find the value of x? H 3 ‾ and 2. Point Q is equidistant from AB ‾. What must be true about Q? AC ​​ ​​ 11 x ​​ ​​ 𝖠 It is on the perpendicular ‾. bisector of AB ​ ​ 6. If you are given the coordinates of A,B,C, and D, how could you prove that ABCD is a rectangle? Select all that apply. 𝖡 It is on the perpendicular ‾. bisector of AC ​ 𝖢 𝖣 ​ BQ = CQ 𝖠 Use the slope formula to show It is on the angle bisector of ∠BAC. ‾, BC ‾ ‖ AD ‾ ‖ CD ‾, and that AB ‾ ⊥ BD ‾. AC ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ 𝖡 Use the distance formula to 3. Which is the converse of the statement? show that AB = CD, BC = AD, and AC = BD. If a polygon has four sides, then it is a quadrilateral. 𝖢 𝖠 If a polygon is not a quadrilateral, then it does not have four sides. Use the distance formula to show that AB = CD and BC = AD, and use the midpoint formula ‾ to show that the midpoint of AC ‾ are the and the midpoint of BD same point. ​ ​ 𝖡 If a polygon is a quadrilateral, then it has four sides. 𝖣 𝖢 𝖣 If a polygon does not have four sides, then it is a quadrilateral. If a polygon does not have four sides, then it is not a quadrilateral. Geometry ​ Use the distance formula to show that AB = CD, and use the slope formula to show that ‾ and AB ‾. ‾ ‖ CD ‾ ⊥ BC AB ​ ​ ​ ​ ​ ​ ​ ​ 𝖤 Use the slope formula to show ‾, and use the ‾ ‖ CD that AB distance formula to show that AB = CD and AC = BD. ​ 1 of 6 ​ ​ ​ ​ 7. What is the value of x? 11. Which point is the center of the circle that contains the vertices of a triangle? x° 64° 𝖠 the point of intersection of the altitudes 𝖡 the point of intersection of the perpendicular bisectors of the sides the point of intersection of the angle bisectors 𝖢 8. What additional piece of information is needed to prove the triangles congruent by ASA? the point of intersection of the medians 𝖣 S T 12. Points A, B, and C are collinear. You are given AC = 18 and BC = 4. What is the value of AB? J D B 13. Consider the figure. Does the figure have the types of symmetry shown in the chart? ​ ​ ​​ _ ‾ JT ≅ SD ​ ​ ‾ ‾ TB ≅ DP ​ 𝖢 𝖣 ​​ 𝖠 ∠T ≅ ∠D 𝖡 ∠J ≅ ∠S ​​ P h 9. Tamira surveyed her classmates to find out how many movies they had seen in the last month. Complete the probability distribution table. Number of Movies Seen in Past Month Number 0 1 2 3+ Frequency 2 8 7 3 g m n Relative Frequency (%) 10. Jack’s eyes are 5 feet above the ground. He is standing 400 feet from the base of a building. The angle of elevation of his line of sight to the top of the building is 67°. How tall is the building? Reflectional symmetry with line h Reflectional symmetry with line g Reflectional symmetry with line m 𝖣 𝖢 𝖠 161 ft 𝖡 175 ft Reflectional symmetry with line n 90° rotational symmetry 120° rotational symmetry 373 ft 180° rotational symmetry 947 ft Geometry 2 of 6 Yes No ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ 17. What is the value of x? 85° ​​ ​​  ​​ 14. The cone-shaped game piece is made of a metal with a mass of 9.2 g/cm 3. What is the mass of the game piece? 92° x° 53° 5 cm 4 cm 18. What rigid motion maps the solidline figure onto the dotted-line figure? 3 cm 108.4 g 231.2 g 15. Libby eats oatmeal, pancakes, or eggs, and she drinks apple juice or orange juice. If she picks a food and a drink at random, what is the probability that she will have oatmeal and apple juice? 6 ​​  ​​ ​​  1 __ 20. Which is an equation for the circle? 8 ​​ 1 __ ​​  ​​ 𝖢 𝖣 ​​ 𝖠 __​13 𝖡 __​15 19. An arc on a circle of radius 10 has 49π an arc length of ___ . What is the 9 measure of the corresponding central angle? y 4 16. Which statements are always true about ABCD? Select all that apply. B ​​ 𝖣 𝖢 𝖠 86.7 g 𝖡 92.6 g 2 x C –8 –6 –2 O –4 2 –2 E –4 D –6 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ 3 of 6 ​ ​ ​ ​ ​ ​ ​ ​ ­ ​ ​ ​ Geometry (x + 4) 2 + (y + 2) 2 = 17 ​ 𝖣 ​​ ​​ ​​ 𝖣 (x – 4) 2 + (y – 2) 2 = √17 ​ 𝖢 m∠ABC + m∠BCD = 180° AB CD 𝖤 ‾ ​ ≅‾ ​ ​ ​​ ___ ​​ ​​ ​​ 𝖠 (x – 4) 2 + (y – 2) 2 = 17 𝖡 (x + 4) 2 + (y + 2) 2 = 5 𝖢 ​​ ​​ 𝖠 ∠ABC ≅ ∠CDA BD AC 𝖡 ‾ ​ ⊥‾ BE ≅ ‾ ED ​‾ ​ A 21. Which figure is being constructed? G 24. A rectangle is rotated about one of its sides. What three-dimensional figure is generated? 𝖠 rectangular prism 𝖡 rectangular pyramid 𝖢 cylinder 𝖣 cone H 𝖠 copy of a segment 𝖡 copy of an angle 𝖢 angle bisector 𝖣 perpendicular bisector 25. What is DF? E F 8 H 22. Which is an expression for the area of △ABC? 3 G D B 67° 48° 26. Which angles are supplementary to ∠4? Select all that apply. C 15 1 2 4 3 6 5 8 7 A ​​ 15 sin 65° · 15 · sin 48° 𝖠 ​_________ 2 sin 67° 𝖠 ∠1 𝖡 ∠2 𝖢 ∠5 𝖣 ∠6 𝖤 ∠7 ​​ 𝖡 ________ ​2 sin1548° · sin 67° ​​ 15 sin 67° · 15 · sin 48° 𝖢 ​_________ 2 sin 65° ​​ 15 sin 65° · sin 67° 𝖣 ​_________ 2 sin 48° 23. Points X(6, 8), Y(3, 3), and Z(13, –3) form a triangle. What is the area of △XYZ? Geometry 4 of 6