Lauretta J. Fox
The diagonal of a parallelogram divides the figure into two congruent triangles.
(figure available in print form)
Given: ABCD is a parallelogram.
Prove: ’ ABD Å ’ CDB
1. In ’ ABCD AB= DC and DA =CB
2. DB = DB
3. ’ ABD Å ’ CDB
1. Opposite sides of a are equal.
2. Reflexive property
3. SSS
Since the parallelogram ABCD is divided into two congruent triangles, the area of each triangle is equal to one half the area of the parallelogram.
Area of parallelogram ABCD =Area of ’ ABD + Area of ’ CDB Area of parallelogram ABCD =2 x Area of ’ ABD
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bh =2 x Area of ’ ABD
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1/2 bh =Area of ’ ABD
The area of a triangle equals one half the product of its base and altitude. A= 1/2 bh
Example
1: Find the area of a triangle whose base is 24 cm. and whose altitude is 15 cm.
Solution
: A- 1/2 bh:A= 1/2 x 24 x 15 = 180 sq. cm.
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Example
2
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Find the altitude of a triangle whose area is 126 sq. ft. and whose base is 42 ft.
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Solution
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1/2 bh= A 1/2 x 42 x h =126 21h = 126 h = 6 ft.
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Fill in the missing information for each triangle.
(figure available in print form)
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5. Find the area of a right triangle whose legs measure 15 cm. and 20 cm. respectively.
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6. What is the area of an equilateral triangle whose side measures 8 inches?
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7. Find the area of triangle ABC if angle A is 30— AB=27 ft. and AC = 34 ft.
(figure available in print form)
8. measures 26 in. and one leg measures 2 ft.
