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Therefore, the measure of ?A is 40°. 3. In isosceles trapezoid ABCD, AC = 4x + 4 and BD = 2x + 10. What is the length of AC? Solution: Step 1: The diagonals of an isosceles trapezoid are congruent. Hence, AC ? BD. Then, AC = BD (Congruent segments have equal lengths) Step 2. Substitute 4x + 4 for AC and 2x + 10 for BD. 4x + 4 = 2x + 10 4x - 2x = 10 - 4 2x = 6 x = 3 Step 3: Substitute 3 to AC = 4x + 4 = 4(3) + 4 = 12 + 4 = 16. Therefore, the length of AC is 16. III. Learning Tasks: Answer the following problems below. 1. KLMN is a trapezoid with median OP. a. If OP = 22, NM = x + 4, and KL = x + 8, what is NM? b. If OP = 24, NM = x - 3 and KL = x + 7, what is KL? 2. ABCD is an isosceles trapezoid. a. If m?A = 2x + 10 and m?B = 3x - 20 what is m?A? b. If m?A = 2x + 15 and m?B = 4x - 11 what is m?B? c. If m?D = x + 15 and m?C = 2x - 85 what is m?D? d. If m?C = 3y + 12 and m?D = 2y + 50, what is m?C?

          Therefore, the measure of ?A is 40°.
3. In isosceles trapezoid ABCD, AC = 4x + 4 and BD = 2x + 10. What is the length of AC?
Solution:
Step 1: The diagonals of an isosceles trapezoid are congruent. Hence, AC ? BD. Then, AC = BD (Congruent segments have equal lengths)
Step 2. Substitute 4x + 4 for AC and 2x + 10 for BD.
4x + 4 = 2x + 10
4x - 2x = 10 - 4
2x = 6
x = 3
Step 3: Substitute 3 to AC = 4x + 4 = 4(3) + 4 = 12 + 4 = 16.
Therefore, the length of AC is 16.
III. Learning Tasks:
Answer the following problems below.
1. KLMN is a trapezoid with median OP.
a. If OP = 22, NM = x + 4, and KL = x + 8, what is NM?
b. If OP = 24, NM = x - 3 and KL = x + 7, what is KL?
2. ABCD is an isosceles trapezoid.
a. If m?A = 2x + 10 and m?B = 3x - 20 what is m?A?
b. If m?A = 2x + 15 and m?B = 4x - 11 what is m?B?
c. If m?D = x + 15 and m?C = 2x - 85 what is m?D?
d. If m?C = 3y + 12 and m?D = 2y + 50, what is m?C?

Therefore, the measure of ?A is 40°.
3. In isosceles trapezoid ABCD, AC = 4x + 4 and BD = 2x + 10. What is the length of AC?
Solution:
Step 1: The diagonals of an isosceles trapezoid are congruent. Hence, AC ? BD. Then, AC = BD (Congruent segments have equal lengths)
Step 2. Substitute 4x + 4 for AC and 2x + 10 for BD.
4x + 4 = 2x + 10
4x - 2x = 10 - 4
2x = 6
x = 3
Step 3: Substitute 3 to AC = 4x + 4 = 4(3) + 4 = 12 + 4 = 16.
Therefore, the length of AC is 16.
III. Learning Tasks:
Answer the following problems below.
1. KLMN is a trapezoid with median OP.
a. If OP = 22, NM = x + 4, and KL = x + 8, what is NM?
b. If OP = 24, NM = x - 3 and KL = x + 7, what is KL?
2. ABCD is an isosceles trapezoid.
a. If m?A = 2x + 10 and m?B = 3x - 20 what is m?A?
b. If m?A = 2x + 15 and m?B = 4x - 11 what is m?B?
c. If m?D = x + 15 and m?C = 2x - 85 what is m?D?
d. If m?C = 3y + 12 and m?D = 2y + 50, what is m?C?

Added by James E.

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