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Transcript
Unit 6H Test Name_____________________ Period______ Read all of the questions carefully. All work must be shown under the appropriate problem to receive full credit. 2 points each unless specified. 60 points total. 1. If you rotate ΔRST 180 about point U, the most specific name for the resulting quadrilateral is: S A) Parallelogram U B) Rhombus C) Rectangle V x R D) Trapezoid o T 2. Parallelogram ABCD is given below. What is the value of x? A) 2 11x + 9 A B) 3 C) 6 D) 16 B 31 D C 6(x + 4) 3. Figure ABCD is a rhombus. What is mBAC ? B A A) 25 25º B) 50 C) 65 D) 75 D C 4. Which of the following is not a characteristic of all rectangles? A) Consecutive angles are supplementary B) Diagonals are perpendicular C) Diagonals bisect each other D) Opposite angles are congruent 5. Given rectangle NOPQ , if the mPNO 23 then the mPNQ is: A) 23 O N B) 46 Z C) 67 D) 75 Q P ____ 60 6. The figure below is a kite. Solve for x. 3x 17 A) 39 B) 13 C) 22 22 D) 15 7. Use the Venn diagram. A quadrilateral ABCD has 4 lines of symmetry. Identify the area of the diagram in which ABCD resides. Quadrilaterals I Parallelograms II Rhombi Squares Rectangles III IV V Trapezoids VI VII Kites A) III B) IV C) V D) VII For # 8-10 use the diagram and given information to solve. N, M, and O are midpoints. MO = 3x + 7, GI = 7x +6, and GM = 5x - 6 G 8. Find GI. __________ N M 9. Find MO. __________ H 10. Find NO. __________ O I B 11. What are the values of the variables in parallelogram ABCD? C 4x + 6 6x - 8 x = ___________ 5y + 16 D A y = ___________ 12. Rectangle NOPQ O N QO = 10x – 8 NZ = 3x + 6 x = __________ Z QO = ____________ P Q 13. Rhombus ABCD B A AB = 10x – 4 BC = 4x + 8 AE = x E AC = _________ Perimeter of ABCD = __________ D C 14. In DEF , E is a right angle and mF 50 . Which list shows the sides in order from shortest to longest? A) DE , EF , FD B) DE , FD , EF C) FD , DE , EF D) EF , DE , FD 15. A triangle has two sides that have lengths of 4 cm and 14 cm. Which could represent the length of the third side of the triangle? A) 3 cm B) 10 cm C) 17 cm D) 18 cm 16. and M L K . Determine if the quadrilateral must be a parallelogram. Justify your answer. N A) No. Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not met. B) Yes. Opposite angles are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram. C) Yes. Opposite sides are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram. D) Yes. One set of opposite sides are congruent, and one set of opposite angles are congruent. This is sufficient evidence to prove that the quadrilateral is a parallelogram. 17. JKLM is a rhombus. If , what is the value of ? Grid your answer correctly. 18. The triangle below shows a point of concurrency. The interior segments are angle bisectors. What is the name of the point of concurrency in the triangle? ___________________________ 19. Complete the proof. (5 points) Given: , Prove: 20. Write the slope-intercept form of the equation of the line through the given points: (-3, -1) and (-5, 5) A) 𝑦 = 3𝑥 − 10 B) 𝑦 = −3𝑥 + 10 C) 𝑦 = −3𝑥 − 10 D) 𝑦 = 3𝑥 + 10 21. What would best describe the following two lines? 1) 6𝑥 + 8𝑦 = 12 2) −4𝑥 + 3𝑦 = 20 A) Parallel B) Perpendicular C) Neither D) Same Line In questions 9–11, use the diagram of a scalene where M is the midpoint of AB . (2 pts. each) k g C h B A M 22. The incenter of ABC lies on which line? _________ 23. The circumcenter of ABC lies on which line? _________ 24. The centroid (center of mass) of ABC lies on which line? _________ 25. In the diagram, 𝑚∠5 = 110° 𝑎𝑛𝑑 𝑚∠6 = 110°. Explain why 𝑝 ∥ 𝑞. Include the name of the Theorem used. p q 5 6 26. A figure is reflected across the y axis, then reflected across the line y=x. Which single transformation results in the same image? A) a rotation 45° B) a rotation -45° C) a rotation 90° D) a rotation -90° E) a rotation 180° 27. The statements for a proof are given below. Given: NO PM NO PM Prove: OP MN O P N M Proof: STATEMENTS REASONS 1. NO PM , NO PM 2. ONP MPN 1. Given 3. NP NP 4. MPN ONP 5. OP MN 2. 3. 4. 5. What reason makes the statement in Step 4 true? A) side-angle-side (SAS) B) side-side-side (SSS) C) corresponding parts of congruent triangles are congruent (CPCTC) D) angle-side-angle (ASA) 28. Solve for x and the measure of the exterior angle. (2 pts) x = ___________________ (1 pt) exterior angle measure = _______________