Angle-Side Relationships in Triangles
Explore the fundamental relationships between angles and sides in triangles, including the Triangle Inequality Theorem and the relationship between angle measure and opposite side length.
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Angle-Side Relationships in Triangles
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Read each question carefully and answer to the best of your ability. Show all your work where applicable. Diagrams are not necessarily drawn to scale unless otherwise stated.
1. In triangle ABC, if m∠A = 70°, m∠B = 50°, and m∠C = 60°, which side is the longest?
AB
BC
AC
Cannot be determined
2. Which of the following sets of side lengths CANNOT form a triangle?
3, 4, 5
6, 8, 10
2, 3, 6
7, 7, 7
3. In any triangle, the side opposite the largest angle is the side.
4. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be than the length of the third side.
5. Consider a triangle with angle measures 45°, 60°, and 75°. Order the sides from shortest to longest.
6. Two sides of a triangle have lengths 8 cm and 13 cm. What is the range of possible lengths for the third side?
7. If a triangle is isosceles, then the angles opposite the congruent sides are also congruent.
True
False
8. In a right-angled triangle, the hypotenuse is always the longest side.
True
False
9. In the triangle below, identify the shortest side and the longest side.
Shortest Side:
Longest Side: