University:
University of North Georgia
Course:
MATH 1113H | Honors Precalculus
Academic year:

2022
Views:

144

Pages:

5
Author:

SpaceCadet101

Honors Geometry Midterm Review: PROOFS PAGE (Chps1-7) Name _____________________________________ On a separate sheet of paper, complete the following two-column proofs. These are just examples! Make sure to look over ALL of our highlighted reasons from first semester. 1. 2. Given: ☼Q ∠A is comp. to ∠BCA RP ≅ PS Given: ∠D is comp. to ∠DBC ∠D ≅ ∠BCA Prove: PQ bisects ∠RPS Prove: ∠A ≅ ∠DBC 3. Given: ∠1 ≅ ∠2 ∠1 ≅ ∠3 4. ∠T ≅ ∠ W Given: ∠TSW ≅ ∠XSV ST ≅ SW Prove: FH bisects ∠EFG Prove: SX ≅ SV 5. Given: CE ≅ DF , BD ≅ GE , 6. BD ⊥ CF , GE ⊥ CF Prove: ∆ACF is isosceles WR bisects ∠XWZ Given: XR bisects ∠ZXW ∆ZWX is isos. with baseWX Prove: ∠XWR ≅ ∠RXW 7. 9. Prove: The segments drawn from the midpoint of the 8. base of an isosceles triangle to the midpoints of the legs are congruent. Prove: The line segments joining the vertex angle of an 10. isosceles triangle to the trisection points of the base are congruent. Prove: If the median to a side of a triangle is also an altitude to that side, then the triangle is isosceles. Prove: If two isosceles triangles have the same base, then the line joining the vertices of the vertex angles of the triangles is the perpendicular bisector of the base. 11. Given: 12. ∠AEC ≅ ∠BED Given: AE ≅ ED Prove: ∆ABC is isosceles Prove: AB ≅ CD 13. 14. Given: ☼O ∠DOB ≅ ∠EOA Prove: CD ≅ CE Given: Prove: ST ≅ RV 16. ∠OMP ≅ ∠OPM ∠PMR ≅ ∠MPR Prove: OR ⊥ bis. PM 17. ∠NOT ≅ ∠POV Given: ∠N ≅ ∠P O is a midpoint OD ≅ OE 15. ∠1 ≅ ∠5 ∠ 2 ≅ ∠6 Given: ☼P M is a midpoint of AB Prove: PQ ⊥ AB Given: ∆PRS isosceles (base SR) ∠PRT ≅ ∠PSQ Prove: TR ≅ QS 18. P Given: AB ≅ AC BD ≅ DC Prove: ∠B ≅ ∠C T S Q R 19. Prove: If segments drawn from the midpoint of one side of a triangle perpendicular to the other two sides are congruen, then the triangle is isosceles. 20. Given: AC ≅ BD AB ≅ CD Prove: ∠B ≅ ∠C 21. Given: ∠ A ≅ ∠E 22. ∠EBC ≅ ∠FCB Given: ∠ABF ≅ ∠DCE FA ≅ FE CH ≅ FB Prove: CF bisects ∠BCD Prove: ∆EHC isosceles 23. 24. 25. PB ⊥ m Given: Prove: PA ≅ PC ∆ABC is isosceles 26. EB ≅ DF 27. Given: AG ≅ GC ∠EAG ≅ ∠FCG Prove: ABCD parallelogram 28. 29. ∠A ≅ ∠X Given: ∠AVZ ≅ ∠XYB ∠ZVB ≅ ∠YBX Prove: VBYZ parallelogram 30. 31. Given: AD median , ∠ADC ≠ ∠ADB Prove: AC ≠ AB 32. 33. 34. 35. 36. PR ≅ PU Given: QR ≅ QU RS ≅ UT Prove: ∠1 ≅ ∠2 38. 37. AD ≅ BC Given: AF ≅ EC BD ⊥ AF , BD ⊥ EC Prove: AB ≅ DC

Chapters 1-7 Midterm Review Proofs

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