Exam (elaborations) Common Core Geometry Cumulative

Triangle JKL is equilateral. One side of the triangle, JL, is a diameter of circle M. Which is true about line segments JK and KL? Both segments are tangent to circle M but are not chords. One segment is tangent to circle M and one segment is a chord in circle M. Both segments are chords in circle M but are not tangents. Neither segment is a chord nor tangent to circle M. - ANSWER Neither segment is a chord nor tangent to circle M. The hypotenuse of a 45°-45°-90° triangle measures in. What is the length of one leg of the triangle? A B C D - ANSWER B A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches. Which could be the lengths of the diagonals of the rhombus? 2 in. by 12 in. 4 in. by 11 in. 6 in. by 8 in. 8 in. by 9 in. - ANSWER 6 in. by 8 in. The law of cosines is used to find the value of m. m2 = 272 + 182 - 2(27)(18)cos(28°) m2 = 729 + 324 - (972)cos(28°) m2 = 1053 - (972)cos(28°) To the nearest whole number, the value of m is - ANSWER 14 Given: RT ≅ TV and ST ≅ TU Prove: RSVU is a parallelogram. 1. RT ≅ TV; ST ≅ TU 1. given 2. ∠RTS and ∠VTU are vert. ∠s; ∠RTU and ∠VTS are vert. ∠s 2. definition of vertical angles 3. ∠RTS ≅ ∠VTU; ∠RTU ≅ ∠VTS 3. vertical angles are congruent 4. ? 4. SAS congruency theorem 5. ∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV 5. CPCTC 6. ∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles 6. definition of alternate interior angles 7. RS ∥ UV and RU ∥ SV 7. converse of the parallelogram diagonal theorem 8. RSVU is a parallelogram 8. definition of parallelogram What is the missing statement in step 4? △RTS ≅ △VTU and △RTU ≅ △VTS △RTS ≅ △RVS and △RTU ≅ △STV △VRS ≅ △VRU and △USR ≅ △USV △VUR ≅ △VUS and △UVS ≅ △SRU - ANSWER △RTS ≅ △VTU and △RTU ≅ △VTS The diagonals of a parallelogram are congruent. Which could be the parallelogram? trapezoid rectangle kite