Angle-Side Relationships in Triangles
Explore the fundamental relationships between angles and sides in triangles, including the Triangle Inequality Theorem and properties of isosceles and scalene triangles at a Grade 12 level.
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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 for full credit.
1. In triangle ABC, if angle A = 30°, angle B = 70°, and angle C = 80°, which side is the longest?
Side AB
Side BC
Side AC
Cannot be determined
2. Which of the following sets of side lengths CANNOT form a triangle?
3, 4, 5
6, 7, 10
2, 3, 6
5, 5, 5
3. In a 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 side lengths 8 cm and 15 cm. What is the range of possible lengths for the third side?
6. If two sides of a triangle are congruent, then the angles opposite those sides are also congruent.
True
False
7. In triangle XYZ, angle X = (3x + 10)°, angle Y = (2x - 5)°, and angle Z = (x + 15)°. Determine the measure of each angle and then order the sides from shortest to longest.
8. Observe the triangle below. Given the angle measures, determine the correct order of the side lengths from smallest to largest.
Order of sides (smallest to largest):