7.5 and 7.6 - Copy

7.5 and 7.6 - Copy - 7-5 Inequalities in a Single Triangle...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7-5 Inequalities in a Single Triangle 7-6 The Distance Between a Line and a Point. The Triangle Inequality A) Theorem 7-5 a. If two sides of a triangle are not congruent, then the angles opposite them are not congruent and the larger angle is opposite the longer side b. Proof: i. ii. Given: Prove: ABC AB AC C C B 1) 2) 3) 4) ABC AB AC 1) Given Let D be a point of mABD = mABC + mCBD ABD D AC , such that AD = AB 2) Point Plotting th. 3) 4) 5) 6) 7) 8) 5) mABC ABD 6) ABC D 7) D ACB 8) ABC ACB B) Theorem 7-6 a. If two angles of a triangle are not congruent, then the sides opposite them are not congruent and the longer side is opposite the larger angle i. If ii. Then 1. b. Example) i. Number 1 from the homework ii. 1. 2. GH KH KH GK 1) 2) 3) 4) Given: KH GK Prove: H is the smallest in the triangle 1) Given 2) 3) 4) GH KH C) Theorem 7-7 (The First Minimum Theorem) a. The shortest segment joining a point to a line is the perpendicular segment b. Proof: i. Given: PQ L at Q and R is any other point of L ii. Prove: PQ C PR 1) 2) 3) 4) 5) Q and R is any other point of L Q is a right angle R is acute R Q PQ C PR PQ L at 1) Given 2) 3) 4) 5) D) Definition a. Distance i. Between a line and an external point is the length of the perpendicular segment from the point to the line. The distance between a line and a point on the line is defined to be zero E) Can any set of three segments form a triangle? F) Theorem 7-8 (The Triangle Inequality) a. The sum of the lengths of any two sides of a triangle is greater than the length of the third side b. Example) i. Can the following sets of numbers be the lengths of the sides of a triangle? 1. 3, 5, 8 2. 2, 2, 3 3. 8, 3, 9 ...
View Full Document

This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State.

Page1 / 4

7.5 and 7.6 - Copy - 7-5 Inequalities in a Single Triangle...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online