Question

NO LINKS!!!
Please help me with #9, 10, and 12

Answer 1

• 9) 130 units;
• 10) m∠1 = 36°, m∠2 = 56°, m∠3 = 124°, m∠4 = 88°, m∠5 = 36°;
• 12) x = 8.

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All three question involve midsegments.

Properties of a midsegment:

• Midsegment is connecting midpoints of two sides;
• Midsegment is parallel to opposite side of the triangle;
• Midsegment is half the length of the parallel side.

Question 9

Perimeter is the sum of side measures.

Side measures are:

• MP = 2QR = 2*25 = 50
• NP = 2QS = 2*22 = 44

• MN = 2SR
• 5x - 34 = 2(x + 4)
• 5x - 34 = 2x + 8
• 5x - 2x = 8 + 34
• 3x = 42
• x = 14

• MN = 5*14 - 34 = 70 - 34 = 36

Perimeter of ΔMNP is:

• 50 + 44 + 36 = 130

Question 10

Corresponding angles are congruent:

• m∠1 = m∠5 and m∠2 = 56°

Linear pair adds up to 180°:

• m∠5 = 180° - 144° = 36° and therefore m∠1 = 36°;
• m∠3 = 180° - 56° = 124°

Find m∠4 using triangle sum theorem:

• m∠4 = 180° - (36° + 56°) = 88°

Question 12

The two angles are congruent as corresponding angles:

• 9x - 23 = 6x + 1
• 9x - 6x = 1 + 23
• 3x = 24
• x = 8