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Q1. If the coordinates of the vertices of triangle PQR are P(1, 2), Q(4, 6), and R(1, 6), what is the length of side PQ?
Solution:
Using the distance formula, PQ = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.
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Q2. In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a right triangle?
Solution:
Triangle XYZ is a right triangle because 5² + 12² = 25 + 144 = 169 = 13².
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Q3. If the coordinates of the vertices of triangle ABC are A(1, 2), B(4, 6), and C(1, 6), what is the length of side AB?
Solution:
Using the distance formula, AB = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.
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Q4. If two triangles are congruent, which of the following must be true?
Solution:
If two triangles are congruent, all corresponding sides and angles are equal, which implies they have the same area and perimeter.
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