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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.


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


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


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.


In the diagram, 𝐴𝐵=6 and 𝐵𝐷=5.

Find 𝐴𝐶.

Find 𝐶𝐷.


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


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


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


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


Determine whether 𝐴𝐸 is a perpendicular bisector of 𝐵𝐶.

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


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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