Explore the properties of isosceles triangles, and learn triangle inequality rules relating sides and angles.
In an isosceles triangle, the angles opposite the two equal sides are also equal. The converse is also true: if two angles are equal, the sides opposite them are equal.
A triangle has two sides of 8 cm and a third side of 6 cm. What can be said about its angles?
The angles opposite the two 8 cm sides are equal, since the triangle is isosceles
A triangle has two angles both equal to 50°. Is it isosceles?
Yes, since two equal angles mean the sides opposite them are also equal
A triangle has angles 70°, 70°, and 40°. Is it isosceles? Which sides are equal?
Yes; the sides opposite the two 70° angles are equal
In any triangle, the sum of any two sides is greater than the third side, and the side opposite a larger angle is longer.
Can a triangle have sides 3 cm, 4 cm, 8 cm?
No, because 3+4=7, which is less than 8
In a triangle, angle A=70°, angle B=50°, angle C=60°. Which side is the longest?
The side opposite angle A (70°, the largest angle) is the longest — side BC
Can a triangle have sides 4 cm, 5 cm, 10 cm?
No, because 4+5=9, which is less than 10
1. A triangle has two equal angles of 65° each. Is it isosceles? What is the third angle?
2. Can a triangle have sides 5 cm, 6 cm, 12 cm?
3. In a triangle, sides are 7,7,10 cm. Which two angles are equal?
4. A triangle has angles 80°, 60°, 40°. Which side is the shortest?
5. Can a triangle have sides 6 cm, 6 cm, 6 cm? What type of triangle is this?
6. A triangle has two equal sides of 9 cm. What can be said about the angles opposite them?
7. Can a triangle have sides 7 cm, 8 cm, 16 cm?
8. In a triangle, sides are 6, 6, 9 cm. Which two angles are equal?
9. A triangle has angles 90°, 45°, 45°. Which two sides are equal?
10. Can a triangle have sides 10 cm, 10 cm, 20 cm?