#6.6 Inequalities in Two Triangles

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If two sides of one triangle are congruent to two sides of another triangle, what can be said about the angles opposite those sides?

Back

The angles opposite the congruent sides are also congruent.

Tags

CCSS.HSG.CO.C.9

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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

In triangle ABC, if angle A is greater than angle B, what can be said about the lengths of sides opposite those angles?

Back

The side opposite angle A (side BC) is longer than the side opposite angle B (side AC).

Tags

CCSS.HSG.CO.C.10

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Tags

CCSS.HSG.CO.C.10

Front

Back

Side a (opposite angle A) is longer than side b (opposite angle B).

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.8.G.A.2

Front

How can you determine if two triangles are congruent?

Back

Two triangles can be determined to be congruent using criteria such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg for right triangles).

Tags

CCSS.HSG.SRT.B.5

Front

What is the significance of the included angle in triangle comparisons?

Back

The included angle is the angle formed between two sides of a triangle. It is significant because it affects the length of the opposite side; a larger included angle results in a longer opposite side.

Tags

CCSS.HSG.CO.C.11

Front

Back

If segment KL is longer than segment MN, then the angle opposite segment KL is larger than the angle opposite segment MN in the respective triangles.

Tags

CCSS.HSG.CO.C.10