Geometry CP - Chapter 3 Test Review PDF
Document Details
Tags
Summary
This document is a review key for a geometry chapter 3 test. It covers various topics, including the classification of angle pairs, finding unknown values (x) in diagrams, and proofs related to parallel lines. The review key answers different questions on the topic.
Full Transcript
## Geometry CP - Chapter 3 Test Review ### Think of each segment in the diagram as part of a line. Which line(s) or plane(s) appear to fit the description? 1. Line(s) parallel to AB: DC, HG, EF 2. Line(s) perpendicular to BF: EF, FG 3. Line(s) skew to CD and containing point E: AE 4. Plane(s) per...
## Geometry CP - Chapter 3 Test Review ### Think of each segment in the diagram as part of a line. Which line(s) or plane(s) appear to fit the description? 1. Line(s) parallel to AB: DC, HG, EF 2. Line(s) perpendicular to BF: EF, FG 3. Line(s) skew to CD and containing point E: AE 4. Plane(s) perpendicular to plane ABE: ADE, HEF, ADC, BCG 5. Plane(s) parallel to plane ABC: HEF ### Classify each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior, or consecutive exterior. Then identify the transversal. | Angle Pair | Classification | Transversal | |---|---|---| | ∠1 and ∠29 | Corresponding | _p_ | | ∠28 and ∠13 | Consecutive interior | _r_ | | ∠26 and ∠16 | Alternate exterior | _s_ | | ∠24 and ∠10 | Alternate interior | _f_ | | ∠28 and ∠16 | Corresponding | _q_ | | ∠10 and ∠13 | Consecutive interior | _s_ | ### For the following diagrams, find the value of x. 1. **Diagram 1:** x = -8, 7 2. **Diagram 2:** x = 56 3. **Diagram 3:** x = 48 4. **Diagram 4:** x = 77, y = 28 5. **Diagram 5:** x = 110, y = 28 6. **Diagram 6:** x = 40, y = 25.3 ### Find the value of x so that n || m. State the theorem or postulate that justifies your solution. 1. **Diagram 1:** x = 24, **Alternate Exterior Angles Converse Theorem** 2. **Diagram 2:** x = 5, **Corresponding Angles Converse Postulate** 3. **Diagram 3:** x = 15.615, **Consecutive Interior Angles Converse Theorem** ### Can you prove that lines p and q are parallel? If so, state the theorem or postulate that you would use. 1. **Diagram 1:** **Yes**, **Corresponding Angles Converse Postulate** 2. **Diagram 2:** **Yes**, **Alternate interior angles Converse Theorem** 3. **Diagram 3:** **No** ### Find the value of x, y, and z given that a || b. * x = 50 * y = 23 * z = 25 ### Find the measure of each angle if m∠1=135°. * m∠2 = 45° * m∠3 = 135° * m∠4 = 90° * m∠5 = 45° * m∠6 = 135° * m∠7 = 45° * m∠8 = 90° ### Given: _l_ || _m_, ∠1 ≅ ∠11. Prove: _l_ || _m_ 1. _l_ || _m_, ∠1 ≅ ∠11: Given 2. ∠1 ≅ ∠15: Alternate Exterior Angle Theorem 3. ∠5 ≅ ∠1: Transitive Property of Congruence 4. _l_ || _m_: Alternate Interior Angles Converse Theorem ### Given: _l_ || _m_, m∠1 + m∠12 = 180°. Prove: _l_ || _m_ 1. _l_ || _m_, m∠1 + m∠12 = 180°: Given 2. ∠1 ≅ ∠15: Alternate Exterior Angle Theorem 3. m∠1 = m∠15: Definition of Congruent Angles 4. m∠15 + m∠12 = 180°: Substitution Property of Equality 5. _l_ || _m_: Consecutive Interior Angles Converse Theorem ### Given: AB ⊥ BD and CD ⊥ BD. Prove: AB || CD 1. AB ⊥ BD, CD ⊥ BD: Given 2. ∠1 is a right angle, ∠2 is a right angle: Definition of Perpendicular Lines 3. m∠1 = 90°, m∠2 = 90°: Definition of Right Angle 4. m∠1 = m∠2: Substitution Property of Equality 5. ∠1 ≅ ∠2 : Definition of Congruent Angles 6. AB || CD: Corresponding Angles Converse Postulate.
