Lines, Angles, and Triangles Flashcards

In similar triangles ABC and DEF, AB/DE = 4/7. The perimeter of triangle ABC is 24. What is the perimeter of triangle DEF?

Answer: 42

Perimeters are in the same ratio as sides: perimeter DEF = 24 × (7/4) = 42.

A reflex angle and its non-reflex counterpart at the same vertex sum to 360°. If the non-reflex angle is 85°, what is the reflex angle?

Answer: 275°

Reflex angle = 360° − 85° = 275°.

In triangle PQR, PQ = PR = 11 and QR = 10. What is the area of the triangle?

Answer: 6√96 cm²

Height from P to QR: h = √(11² − 5²) = √(121−25) = √96; area = ½(10)(√96) = 5√96.

Two parallel lines are cut by a transversal. The angle formed above line m on the right is 63°. What is the co-interior angle below line n on the right?

Answer: 117°

Co-interior angles (same-side interior) are supplementary: 180° − 63° = 117°.

Which of the following sets of angles CANNOT be the angles of a triangle?

Answer: 91°, 89°, 1°

91 + 89 + 1 = 181° ≠ 180°, so these cannot form a triangle.

Two lines meet at a point forming four angles. One angle is 42°. What are the measures of the other three angles?

Answer: 138°, 42°, 138°

Vertical angle = 42°; adjacent supplementary angles = 180° − 42° = 138°; so the four angles are 42°, 138°, 42°, 138°.

In right triangle ABC with right angle at C, AC = 8 and BC = 15. What is the area of the triangle?

Answer: 60

Area = ½ × base × height = ½(8)(15) = 60.