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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.
- 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.
Given isosceles trapezoid ABCD, 𝐵𝐶 ∥ 𝐴𝐷. If 𝑚 < 𝐴 = 4𝑥 − 3 and 𝑚 < 𝐷 = 2𝑥 + 1, find the value of 𝑥.
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.
- In isosceles trapezoid 𝐴𝐵𝐶𝐷, 𝐴𝐵 ∥ 𝐶𝐷. 𝐴𝐵 = 18, 𝐶𝐷 = 6, and 𝐴𝐷 = 10. Find the length of an altitude of
𝐴𝐵𝐶𝐷.
Review Section:
- Find the equation of a line that is perpendicular to 3𝑥 + 6𝑦 = 18 and passes through the point (6,-8).
- 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.
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
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
