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Isosceles Trapezoid, Exams of Computational Geometry

All the properties of a trapezoid. • Non-parallel sides are congruent. • Diagonals are congruent. • Base angles are congruent.

Typology: Exams

2021/2022

Uploaded on 09/12/2022

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Name:_____________________________________________________________ Date:_________________ Period:__________
Chapter 10: Quadrilaterals
Topic 5: Trapezoid
Trapezoid:
A trapezoid is a quadrilateral that has only one set of parallel sides.
Diagram:
Properties:
Only one set of parallel sides (bases).
The non-parallel sides are called legs.
Isosceles Trapezoid:
Diagram:
Properties:
All the properties of a trapezoid
Non-parallel sides are congruent.
Diagonals are congruent.
Base angles are congruent.
Opposite angles are supplementary.
Word Problems:
1.) The bases of an isosceles trapezoid ABCD measure 10 cm and 20 cm. The height (altitude) is 12 cm. How
long are the legs AB and CD?
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Name:_____________________________________________________________ Date:_________________ Period:__________

Chapter 10: Quadrilaterals

Topic 5: Trapezoid

Trapezoid:

A trapezoid is a quadrilateral that has only one set of parallel sides. Diagram:

Properties:  Only one set of parallel sides (bases).  The non-parallel sides are called legs.

Isosceles Trapezoid:

Diagram:

Properties:  All the properties of a trapezoid  Non-parallel sides are congruent.  Diagonals are congruent.  Base angles are congruent.  Opposite angles are supplementary.

Word Problems:

1.) The bases of an isosceles trapezoid ABCD measure 10 cm and 20 cm. The height (altitude) is 12 cm. How long are the legs AB and CD?

2.) Given: Isosceles trapezoid ABCD with BC ||AD. If m<A = 4x+20 and m<D = 2x+38, find m<A, m<B, m<C, and m<D.

3.) In isosceles trapezoid KIME, <K and <E are the base angles. If IK = 11 and ME = 3x - 1, what is the value of x?

4.) In isosceles trapezoid ABCD, BC||AD. The measure of <ADC=4x+20 and the measure of <DAB = 8x - 20. Find the value of x, <ADC, <DAB, <BCD, and <ABC.

  1. In the accompanying diagram, isosceles trapezoid 𝐶𝐷𝐸𝐹 has bases of lengths 8 and 18 and an altitude

with a length of 12. Find the length of 𝐶𝐷.

  1. Given isosceles trapezoid ABCD, 𝐵𝐶 ∥ 𝐴𝐷. If 𝑚 < 𝐴 = 4𝑥 − 3 and 𝑚 < 𝐷 = 2𝑥 + 1, find the value of 𝑥.

  2. Given isosceles trapezoid 𝐴𝐵𝐶𝐷, 𝐵𝐶 ∥ 𝐴𝐷. If 𝑚 < 𝐴 = 3(2𝑥 − 7) and 𝑚 < 𝐶 = 4𝑥 + 1, find the value of

𝑥. Find the measure of all of the angles.

  1. In isosceles trapezoid 𝐴𝐵𝐶𝐷, 𝐴𝐵 ∥ 𝐶𝐷. 𝐴𝐵 = 18, 𝐶𝐷 = 6, and 𝐴𝐷 = 10. Find the length of an altitude of

𝐴𝐵𝐶𝐷.

Review Section:

  1. Find the equation of a line that is perpendicular to 3𝑥 + 6𝑦 = 18 and passes through the point (6,-8).
  1. In the accompanying diagram of right triangle ABD and DBC, AB=5, AD=4, and CD=1. Find the length of

𝐵𝐶̅̅̅̅, to the nearest tenth.

  1. Which of these lengths could be the sides of a triangle? (1) 15,7,23 (2) 5, 9, 13 (3) 8, 5, 13 (4) 6, 15, 23

  2. In the diagram below, under which transformation will ∆𝐴′𝐵′𝐶′^ be the image of ∆𝐴𝐵𝐶? (1) Rotation (2) Dilation (3) Translation (4) Glide Reflection