Triangles - Properties and Congruence for Exam Success

Triangles - Properties and Congruence - Coordinate Geometry Applications - Problem Set

Q. If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is the length of segment AB?

Solution

Length AB = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: B — 5

Q. In triangle PQR, if angle P = 90 degrees and PQ = 6 cm, PR = 8 cm, what is the length of QR?

Solution

Using the Pythagorean theorem, QR = √(PQ² + PR²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Correct Answer: A — 10 cm

Q. What is the length of the altitude from vertex A to side BC in triangle ABC if the area is 30 cm² and base BC = 10 cm?

Solution

Area = 1/2 * base * height. Therefore, 30 = 1/2 * 10 * height, which gives height = 6 cm.

Correct Answer: B — 5 cm

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