Warm-up

Take a pink paper and get started.

Warm-up

Agenda

5-1/5-2 Review Homework Review 5-3 Indirect Proofs 5-4 Inequalities for sides and angles

5-1 Special Segments

5-1 Special Segments

5-1 Special Segments

5-1 Special Segments

5-1 Review

5-1 Review

5-1 Review

5-1 Review

5-2 Right Triangles

Theorem 5-5 LL (Leg - Leg)

If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.

HA (Hypotenuse - Angle)

If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent.

LA (Leg - Angle)

If the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

HL (Hypotenuse -Leg)

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

5-2 Review

1. LL corresponds to __________

2. AAS corresponds to __________

3. HL corresponds to __________ _____4. ASA corresponds to __________

5-2 Review

1. LL corresponds to SAS.

2. AAS corresponds to HA.

3. HL corresponds to SSS (kinda).

4. ASA corresponds to LA.

5-2 Study Guide

5-2 Practice

5-2 Practice

5-3 Indirect Proof

We have used direct reasoning in the proofs we have encountered up to this point.  When using direct reasoning, we started with a true hypothesis and proved that the conclusion is true.  With indirect reasoning, we will assume that the conclusion is false and then show that this assumption leads to a contradiction of the hypothesis or some other accepted fact, like a postulate, theorem, or corollary.   Then, since our assumption has been proved false, the conclusion must be true.

5-3 Indirect Proof

5-3 Indirect Proof

Given: Points A, B and C are on line l Point P is not on l

PB < PC

Prove: mPCB 90

P

A B C

1.

2.

3.

4.

l

Given: Points A, B and C are on line l Point P is not on l

PB < PC

Prove: mPCB 90

P

A B C

1. Assume PCB = 90

2. Then PC l

3. PC < PB (Contradiction)

4. PCB 90

l

5-3 Definition of Inequality

For any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c.

5-3 Properties of Inequality (p. 254)

5-3 Exterior Angle Inequality Theorem

If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles.

Answers Ahead

5-3 Study Guide

Homework

5-3 Study Guide and Practice