Inequalities Involving Two Triangles SAS Inequality/Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included.

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Presentation transcript:

Inequalities Involving Two Triangles SAS Inequality/Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the third side of the first triangle is longer than the third side of the second triangle.

Example 5-1b Prove: AD < AB Given:m  1 < m  3 E is the midpoint of Write a two-column proof.

Example 5-1b Proof: Statements Reasons 1. Given 2. Definition of midpoint 3. Reflexive Property 4. Given 5. Definition of vertical angles 6. Substitution 7. SAS Inequality E is the midpoint of

Inequalities Involving Two Triangles SSS Inequality If two sides of a triangle are congruent to two sides of another triangle and the third side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle.

Write an inequality using the information in the figure. a. b. Find the range of values containing n. Answer: Example 5-3c Answer: 6 < n < 25

Example 5-2b Given:X is the midpoint of  MCX is isosceles. CB > CM Prove:

Example 5-2b Proof: Statements Reasons 1. Given 2. Definition of midpoint 3. Given 4. Definition of isosceles triangle 5. Given 6. Substitution 7. SSS Inequality X is the midpoint of  MCX is isosceles.