1) IF DE = 9, find BC 2) if m<ADE = 80, then find m< ABC
3) If DE = 2x + 7 , and BC = 7x - 1, find BC

1. BC = 18

2. m<ABC = 80°

3. x = 5

Step-by-step explanation:

1. If DE = 9, therefore:

(based on the midsegment theorem, DE is half the length of the third side, BC)

2. m<ADE = 80°, then,

m<ABC = 80°

This is because m<ADC and m<ABC are corresponding angles. Corresponding angles are congruent.

3. DE = 2x + 7 , and BC = 7x - 1, find BC

Thus:

(midsegment theorem)

(substitution)

Solve for x

Collect like terms

Divide both sides by 3

x = 5

180 square centimeters

step-by-step explanation:

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