Ordering Sides and Angles in Triangles

Front

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

Back

In a triangle, the longer the side, the larger the angle opposite that side. This is known as the Side-Angle Relationship.

Tags

CCSS.HSG.CO.C.10

Front

List the sides of triangle PQR in order from shortest to longest if angle P is the largest angle.

Back

Side QR, Side PR, Side PQ.

Front

What is the significance of 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

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

Back

The longest side is opposite the largest angle.

Tags

CCSS.HSG.CO.C.10

Front

What is the notation used to represent angles in triangle notation?

Back

Angles are typically represented using angle symbols, such as <A, <B, <C for angles at vertices A, B, and C respectively.

Front

If angle M is the largest angle in triangle MON, which side is the longest?

Back

Side ON is the longest side, as it is opposite the largest angle M.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the angles and sides in triangle ECD if angle E is the smallest angle?

Back

Side CD is the shortest side, as it is opposite the smallest angle E.

Tags

CCSS.HSG.CO.C.10

Front

How can you order the angles of a triangle based on the lengths of its sides?

Back

The angles can be ordered from smallest to largest based on the lengths of the opposite sides, with the smallest angle opposite the shortest side.

Tags

CCSS.HSG.CO.C.10

Front

What is the measure of angle E if side CD is the longest side in triangle ECD?

Back

Angle E must be the largest angle in triangle ECD, as it is opposite the longest side CD.

Tags

CCSS.HSG.CO.C.10

Front

Explain how to apply the triangle inequality theorem to determine if three lengths can form a triangle.

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.