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Lesson Worksheet: Corollaries of Isosceles Triangle Theorems Mathematics

In this worksheet, we will practice using the corollaries of the isosceles triangle theorems to find missing lengths and angles in isosceles triangles.

Q1:

For which values of 𝑥 and 𝑦 is 𝐴𝐷 a perpendicular bisector of 𝐵𝐶?

  • A𝑥=2, 𝑦=75
  • B𝑥=23, 𝑦=1
  • C𝑥=43, 𝑦=35
  • D𝑥=2, 𝑦=1
  • E𝑥=83, 𝑦=75

Q2:

In the figure, 𝐴𝐵=𝐴𝐶=10cm, 𝐸𝐵=𝐸𝐶, and 𝐴𝐷𝐵𝐶=𝐷. If 𝐵𝐶=16cm, what are the lengths of 𝐴𝐷 and 𝐷𝐶 respectively?

  • A2 cm, 8 cm
  • B6 cm, 8 cm
  • C12.8 cm, 8 cm
  • D8 cm, 6 cm

Q3:

Fill in the blank: In this figure, if 𝐴𝐵=𝐴𝐶, 𝐴𝐷𝐵𝐶={𝐷}, where 𝐷𝐶=8cm, and 𝑚𝐶𝐴𝐷=𝑚𝐵𝐴𝐷=35, the length of 𝐵𝐷 is cm.

Find 𝑚𝐴𝐶𝐵.

Q4:

In the diagram, 𝐴𝐵=6 and 𝐵𝐷=5.

Find 𝐴𝐶.

Find 𝐶𝐷.

Q5:

In the following figure, if 𝐿𝑋=𝑌𝑋, 𝐿𝑍=𝑌𝑍, 𝑚𝐿𝑌𝑋=30, 𝑚𝑍𝐿𝑌=55, and 𝑀 is the midpoint of 𝐿𝑌, find 𝑚𝑀𝑍𝐿 and 𝑚𝐿𝑀𝑋.

  • A90, 35
  • B35, 55
  • C30, 60
  • D35, 60
  • E35, 90

Q6:

In the following figure, 𝐵𝐷=𝐶𝐸, 𝑚𝐴𝐷𝐵=𝑚𝐴𝐸𝐶=90, and 𝑚𝐴𝐶𝐵=𝑚𝐴𝐵𝐶. If 𝑚𝐷𝐴𝐵=34, find 𝑚𝐴𝐶𝐸.

Q7:

In the following figure, 𝐴𝐶=𝐴𝐵, 𝐴𝐶𝐷𝐹, and 𝐴𝐵𝐷𝐸. If 𝑚𝐴𝐵𝐶=30, find 𝑚𝐸𝐷𝐹.

Q8:

In the figure below, 𝐴𝐶𝐵𝐷=𝑀, 𝑀𝐷=𝑀𝐶, 𝐴𝐵𝐶𝐷, and 𝑚𝑀𝐶𝐷=40. Draw 𝑀𝐸𝐶𝐷 and cut 𝐶𝐷 at 𝐸, then draw 𝑀𝐹𝐴𝐵 and cut 𝐴𝐵 at 𝐹. Find 𝑚𝐶𝑀𝐸 and 𝑚𝐵𝑀𝐹.

  • A40, 50
  • B50, 40
  • C100, 100
  • D40, 40
  • E50, 50

True or False: 𝐸𝐹 is an axis of symmetry for the shape.

  • AFalse
  • BTrue

Q9:

Determine whether 𝐴𝐸 is a perpendicular bisector of 𝐵𝐶.

  • AIt is a perpendicular bisector.
  • BIt is not a perpendicular bisector.

Q10:

In the diagram, 𝐴𝐷 is the perpendicular bisector of 𝐵𝐶. Find the value of 𝑥.

This lesson includes 56 additional questions and 189 additional question variations for subscribers.

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