Triangle Basics
How many sides does a triangle have?
3 sides.
What do we call a triangle with all three sides the same length?
An equilateral triangle.
Two angles that add up to 90° are called what?
Complementary angles.
State the Triangle Inequality Theorem in words.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side
What is the sum of the interior angles of any triangle?
180°
What do we call a triangle with exactly two sides the same length?
An isosceles triangle.
Two angles that add up to 180° are called what?
Supplementary angles.
Can 3, 4, and 8 be the sides of a triangle? Explain
No. 3 + 4 = 7, which is not greater than 8, so it does not form a triangle.
Name the three types of angles that can appear in triangles.
Acute, right, and obtuse angles.
What do we call a triangle with all three sides different lengths?
A scalene triangle.
What do we call a pair of angles that are across from each other when two lines intersect?
Vertical angles
Can 5, 7, and 10 be the sides of a triangle?
Yes. 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5, so it forms a triangle.
What do we call a triangle that has one 90° angle?
A right triangle.
Classify this triangle by its sides and angles: sides are all equal, and each angle is 60°.
Equilateral and acute triangle.
If one angle of a triangle is 50° and another is 60°, what is the third angle?
70° (because 180° − 50° − 60° = 70°).
Two sides of a triangle are 6 cm and 9 cm. What is the smallest and largest possible length for the third side?
It must be greater than 3 cm and less than 15 cm (3 < x < 15).
If a triangle has angles measuring 40° and 65°, what is the measure of the third angle?
75° (because 180° − 40° − 65° = 75°
A triangle has side lengths 5 cm, 5 cm, and 8 cm. Classify it by its sides and by its angles (acute, right, or obtuse).
Isosceles and acute triangle.
An exterior angle of a triangle is 120°. One of the remote interior angles is 50°. What is the measure of the other remote interior angle?
70° (because 50° + x = 120°, so x = 70°).
Two sides of a triangle are 12 cm and 5 cm. Give an example of a whole-number length for the third side that would NOT form a triangle, and explain.
17 cm does not form a triangle because 12 + 5 = 17, which is not greater than 17