Lesson Worksheet: Deductive Proof for Geometric Properties Mathematics

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

Q1:

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

Q2:

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

Q3:

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

  • ATrue
  • BFalse

Q4:

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

  • ATrue
  • BFalse

Q5:

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

  • ATrue
  • BFalse

Q6:

In the given figure, find the measure of 𝑃𝐶𝑄.

Q7:

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

Q8:

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

Q9:

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

Q10:

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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