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Geometry Diagram Analysis with Definitions

Determine the truth of statements in a geometry diagram by applying learned definitions. Identify linear pairs, opposite rays, right angles, supplementary angles, midpoints, and vertical angles.

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Geometry Diagram Analysis with Definitions

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  1. Decide whether each statement about the diagram is true. Explain your answer using the definitions you have learned. a. ACBD b. c. AEBand CEBare a linear pair. EAand EBare opposite rays. EXAMPLE 3 Use definitions

  2. a. This statement is true. The right angle symbol in the diagram indicates that the lines intersect to form a right angle. So you can say the lines are perpendicular. This statement is true. By definition, if the noncommon sides of adjacent angles are opposite rays, then the angles are a linear pair. Because EAand ECare opposite rays, AEBand CEBare a linear pair. b. EXAMPLE 3 Use definitions SOLUTION

  3. c. This statement is false. Point Edoes not lie on the same line as Aand B, so the rays are not opposite rays. EXAMPLE 3 Use definitions

  4. Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. JMFand FMGare supplementary. 7. ANSWER This statement is true : Because linear pairs of angles are supplementary. for Example 3 GUIDED PRACTICE

  5. Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. Point Mis the midpoint of FH. 8. ANSWER This statement is false : Because it is not known that FM = MH . So, you can say that point M is the mid-point of FH for Example 3 GUIDED PRACTICE

  6. Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. JMFand HMGare vertical angles. 9. ANSWER This statement is true : Because in the diagram two intersecting lines form 2 pairs of vertical angles. So, you can say that are vertical angles. JMFand HMG for Example 3 GUIDED PRACTICE

  7. Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. 10. FH JG FH JG ANSWER This statement is false : By definition if two intersect to form a right angle then they are perpendicular. But in the diagram it is not known that the lines intersect at right angles . So you cannot say that for Example 3 GUIDED PRACTICE

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