geometry a (workbook 17.1-workbook 17.2)

workbook 17.1

sides and segments in parallelograms

workbook 17.2

angles in parallelograms

Use the figure and the information to complete the proof. Given: ABCD is a parallelogram. Prove: The diagonals ¯AC¯ and ¯BD¯ bisect each other. © 2016 StrongMind. Created using GeoGebra. Match each statement in the proof with the correct reason.

1. given 2. opposite sides of parallelogram are congruent 3. vertical angles theorem 4. definition of parallelogram 5. alternate interior angles theorem 6. AAS congruence theorem 7. corresponding parts of congruent triangles are congruent 8. definition of midpoint 9. definition of bisect

Examine parallelogram ABCD. Sides ¯CD¯ and ¯AB¯ have lengths of y+18 and 4y, respectively. Determine the value of y and answer the following question. © 2016 StrongMind. Created using GeoGebra. What is the length of ¯AB¯? Enter the correct value.

24

Examine parallelogram ABCD. Angles A and D have measures of x∘ and (x+30)∘, respectively. © 2016 StrongMind. Created using GeoGebra. What is the value of x? Do not include the degree symbol.

75

Examine parallelogram ABCD and carefully read the description of Paola's proof. Given: ¯AB¯∥¯CD¯ and ¯AD¯∥¯BC¯, and ¯AC¯ is a diagonal of both sets of parallel lines. © 2019 StrongMind. Created using GeoGebra. Paola proves that ∠B≅∠D. She first uses Alternate Interior Angles Theorem, then she finds ¯AC¯≅¯AC¯ by the Reflexive Property. Next, Paola uses the ASA Congruence Theorem to show △ABC≅△CDA. Since corresponding parts of congruent triangles are congruent, ∠B≅∠D. Which pairs of angles could Paola have concluded are congruent using the Alternate Interior Angles Theorem?

∠1≅∠2 and ∠3≅∠4