Geometry: Unit 4 Review

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If two sides of a triangle are 2 cm and 1.2 cm, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than the difference of the two sides (0.8 cm) and less than the sum of the two sides (3.2 cm). Therefore, the range is 0.8 cm < third side < 3.2 cm.

Front

In triangle ABC, if angle A is the largest angle, which side is the longest?

Back

Side BC is the longest side because the longest side is opposite the largest angle.

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Front

How do you determine the longest side of a triangle given its angles?

Back

Order the angles from largest to smallest; the side opposite the largest angle is the longest.

Front

What is the formula for the perimeter of a triangle?

Back

The perimeter of a triangle is the sum of the lengths of its sides: P = a + b + c.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

How can you find the range of possible distances between two points in a triangle?

Back

Use the Triangle Inequality Theorem to find the range: the distance must be greater than the difference of the two other sides and less than their sum.

Front

What is the significance of the shortest side in a triangle?

Back

The shortest side is always opposite the smallest angle in the triangle.