Lesson Worksheet: Deductive Proof for Geometric Properties Mathematics

In this worksheet, we will practice proving certain geometric properties using deductive proof.


Two straight lines, 𝐴𝐵 and 𝐶𝐷, intersect at point 𝐸.

Fill in the blank: If the angles 𝐴𝐸𝐷 and 𝐴𝐸𝐶 are adjacent angles where 𝐸𝐶𝐸𝐷=𝐶𝐷, then 𝑚𝐴𝐸𝐶+𝑚𝐴𝐸𝐷=.

Fill in the blank: If the angles 𝐴𝐸𝐶 and 𝐶𝐸𝐵 are adjacent angles where 𝐸𝐴𝐸𝐵=𝐴𝐵, then 𝑚𝐴𝐸𝐶+𝑚𝐶𝐸𝐵=.

True or False: We deduce from the two parts above that 𝑚𝐴𝐸𝐷=𝑚𝐶𝐸𝐵.

  • ATrue
  • BFalse


𝑂𝐴, 𝑂𝐵, 𝑂𝐶, 𝑂𝐷, and 𝑂𝐸 are rays that start at the point 𝑂. The measure of 𝐴𝑂𝐷=80, the measure of 𝐴𝑂𝐵=55, and the measure of 𝐵𝑂𝐸=45.

Do the two rays 𝑂𝐷 and 𝑂𝐸 form a straight line 𝐷𝐸?

  • AYes
  • BNo

True or False: The total sum of the measures of the accumulative angles at the point 𝑂 is 180.

  • ATrue
  • BFalse


True or False: In the given figure, the two straight lines 𝐴𝐵 and 𝐶𝐷 are parallel.

  • ATrue
  • BFalse


True or False: In the given figure, if 𝐷𝐶𝐴𝐵, 𝐸𝐴𝐵, 𝑚𝐸𝐵𝐶=60, and 𝑚𝐴𝐷𝐶=120, then 𝐴𝐷𝐵𝐶.

  • ATrue
  • BFalse


True or False: A straight line that is perpendicular to one of two parallel lines is also perpendicular to the other.

  • ATrue
  • BFalse


In the given figure, find the measure of 𝑃𝐶𝑄.


In the given figure, if 𝐿𝑀𝑁𝑂 is a rectangle, 𝐴𝑁=𝐵𝑀, and the measure of 𝑁𝑀𝐶=50, find the measure of 𝑀𝑁𝐶.


In the given figure, use the properties of congruent triangles to find the measure of 𝐵𝐶𝐷.


In the given figure, 𝑚𝐵𝐴𝐶=𝑚𝐵𝐷𝐶=50 and 𝑚𝐶𝐵𝐷=𝑚𝐴𝐶𝐵=40.

Is the triangle 𝐴𝐵𝐶 congruent with the triangle 𝐷𝐶𝐵?

  • AYes
  • BNo

Is the diagonal 𝐴𝐶 equal to the diagonal 𝐵𝐷?

  • AYes
  • BNo


In the given figure, if 𝑚𝐴𝐷𝐶=𝑚𝐴𝐸𝐵, then which of the following is true?

  • A𝐴𝐷=𝐵𝐸
  • B𝐷𝐶=𝐴𝐸
  • C𝐷𝐶=𝐸𝐶
  • D𝐷𝐵=𝐴𝐸
  • E𝐷𝐶=𝐵𝐸

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