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Geometry Semester 1 Model Problems (California Essential Standards) Short Answer GE 1.0 1. List the undefined terms in Geometry. 2. Match each of the terms with the corresponding example a. A theorem. b. A conjecture. c. An axiom (postulate). d. An undefined term. e. Inductive Reasoning. f. Deductive Reasoning. U. Every student in Mr. Smith’s class drew a quadrilateral, measured the interior angles, and found the sum. They discovered that all of their sums were the same and generalized this was true for every quadrilateral. V. Shelly used a piece of paper as a model of a plane and described it in her notes. W. Rueben found a property of rhombi, but does not know if it can be proven to be true. X. Yasmine noticed that all rectangles have opposite sides congruent and then found a way to prove this was true. Y. Rachel used a property of parallelograms to calculate the lengths of the sides of a polygon on her homework. Z. Andrew noticed that the relationship between corresponding angles has not been proven, but is accepted as true and is used to prove that other angle relationships are true. GE 16.0 3. Given: AB . What is the first step in constructing the perpendicular bisector to AB ? a. b. c. d. 4. Draw a line segment connecting points E and F. From point C, draw an arc that intersects the line at points A and B. Draw a line segment connecting points A and B. From points A and B, draw equal arcs that intersect at points E and F. Darla is constructing an equilateral triangle. Which of the following could be her first step? a. c. b. d. 5. Marsha is using a straightedge and compass to do the construction shown. Which statement best describes the construction Martha is doing? a. a line through P parallel to line l by constructing two lines perpendicular to the same line b. a line through P parallel to line l by copying an angle c. a line through P perpendicular to line l d. a line through P congruent to line l 6. Amina is bisecting an angle. Which of the construction diagrams shown below best represents the beginning of Amina’s construction? c. a. b. d. GE 7.0 7. In the diagram, lines l and m are parallel. What relationship exists between angles A and B? What postulate or theorem supports that relationship? 8. Lines l and m are shown in each diagram. In which diagram MUST lines l and m be parallel? a. b. c. d. 9. For the quadrilateral shown, what is the value of x? 10. In the diagram, quadrilateral TRAP is a trapezoid in which TP RA . What is the value of x? 11. In the diagram shown, what is the value of x? 12. Quadrilateral ABCD is circumscribed by a circle, as shown in the diagram to the right. What is the measure of ∠C? GE 5.0 13. Given: ABCD is a rhombus Which theorem or postulate could be used to prove that AED ≅ AEB ? and AC bisects DB . Prove: AED ≅ AEB 14. In the diagram, ∠A ≅ ∠D and ∠B ≅ ∠E . What additional information would be enough to prove that ABC ≅ DEF ? GE 4.0 15. If LMN and PQR have sides LM ≅ PQ and MN ≅ QR , which pair of angles would need to be congruent to be sufficient to prove that LMN ≅ PQR ? 21. In the diagram, ABC is a right triangle. What is the slope of BC ? 24. Use the proof to answer the question below. Given: AB ≅ BC ; D is the midpoint of AC Prove: ABD ≅CBD STATEMENT 1. AB ≅ BC ; D is the midpoint 1. Given of AC REASON 2. AD ≅ CD 2. Definition of midpoint 3. BD ≅ BD 4. ABD ≅CBD 4. ? 3. Reflexive Property Which triangle equality theorem or postulate can be used as a correct reason for step 4? a. 25. Given: ∠2 ≅ ∠3 Prove: ∠1 ≅ ∠4 Use the proof to answer the question below. STATEMENT 1. ∠2 ≅ ∠3 2. ∠1 ≅ ∠2; ∠3 ≅ ∠4 3. ∠1 ≅ ∠4 REASON 1. Given 2. ? 3. Transitive Property What reason can be used to justify step 2? GS 13.0 33. In the diagram shown, m∠CBD = 95˚. What is the measure of ∠CDB ? 60. The diagram shows a trapezoid with a height of 4 cm. What is the area of the trapezoid? 34. In the diagram shown, P is a point on ML . What is the measure of the angle marked X?