Question

1) IF DE = 9, find BC

Answer 1

Answer:

1. BC = 18

2. m<ABC = 80°

3. x = 5

Step-by-step explanation:

1. If DE = 9, therefore:

$BC = 2 \times 9 = 18$ (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:

$BC = 2 \times DE$ (midsegment theorem)

$7x - 1 = 2 \times (2x + 7)$ (substitution)

Solve for x

$7x - 1 = 4x + 14$

Collect like terms

$7x - 4x = 1 + 14$

$3x = 15$

Divide both sides by 3

x = 5