Triangle Inequality Theorem & Congruent Triangles FLASHCARD

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

List the conditions that must be satisfied for three lengths to form a triangle.

Back

For three lengths a, b, and c to form a triangle, the following must be true: a + b > c, a + c > b, and b + c > a.

Front

Can the lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

Which set of lengths cannot represent the sides of a triangle: {32, 34, 60}, {28, 30, 58}, {13, 20, 27}, {2, 4, 5}?

Back

{28, 30, 58} cannot represent the sides of a triangle.

Front

What are congruent triangles?

Back

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

Front

How can you prove that two triangles are congruent?

Back

Two triangles can be proven 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).

Front

What is the significance of ordering side lengths from shortest to longest?

Back

Ordering side lengths helps to visually assess whether the lengths can form a triangle and to apply the Triangle Inequality Theorem.

Front

If the side lengths of a triangle are 6, 17, and 22, what can you conclude?

Back

These lengths can form a triangle because they satisfy the Triangle Inequality Theorem.

Front

List the angles of a triangle in order from smallest to largest if the measures are ∠A, ∠B, and ∠C.

Back

If ∠A < ∠C < ∠B, then the order is ∠A, ∠C, ∠B.

Front

What is the relationship between the longest side of a triangle and its angles?

Back

The longest side of a triangle is opposite the largest angle.