6.1/6.2 Triangle Inequalities and Congruence

2. A student has an average score of 73 on five tests this

semester. It is later discovered that one of the

tests was graded incorrectly and the score should have

been 91 instead of 81. What is the correct average of the

five tests?A. 74B. 75C. 76D. 83

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to describe the 3rd side, given 2 sides, and

to identify congruent polygons and their corresponding parts.

1.B 8 C

55

What is the height of trapezoid ABCD?

A. 2 unitsB. 3 unitsC.4 unitsD. 6 units

CB

A 14 D

Notes

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to describe the 3rd side, given 2 sides, and to identify congruent polygons and their

corresponding parts

Triangle Inequality Theorems –

A

C

B*The sum of the lengths of 2 sides of a triangle is greater than the length of the 3rd side.

,In ABC ACBCAB ABACBC BCACAB

*One side of a triangle is longer than a 2nd side if and only if the angle opposite the 1st side is larger than the angle opposite the 2nd side.

EX 1 – A gardener wants to make a triangular garden. He has 23 feet of fence with which to form the perimeter of the garden. Can the gardener make a garden with the given side lengths?

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to describe the 3rd side, given 2 sides, and to identify congruent polygons and their

corresponding parts

a. 3 ft, 5 ft, 15 ft? 1553

Can’t be done!

b. 8 ft, 7 ft, 8 ft?

878

887

788

c. 3 ft, 11 ft, 9 ft?

9113 3911

1139

Shortcut??

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to describe the 3rd side, given 2 sides, and to identify congruent polygons and their

corresponding parts

EX 2 – cm. 3.4 and cm 8 ,In VWUVUVW

a. What do you know about the length of ? UW

UWVWUV UW 3.48UW3.12

UVUWVW 83.4 UW

7.3UW

VWUWUV 3.48 UW

7.3UW

Sooo, UW must be between 3.7 and 12.3

b. Sketch 3 possible shapes of UVW

CKC p. 281

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to describe the 3rd side, given 2 sides, and to identify congruent polygons and their

corresponding parts

Congruent Polygons – Same size and shape!

B

D

A HG

O

*Polygons are congruent iff all corresponding parts are congruent

B HA OD G

BA HOAD OG

DB GH

*when naming congruent polygons, list corresponding angles in order!

BAD H O G

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to describe the 3rd side, given 2 sides, and to identify congruent polygons and their

corresponding parts

EX 3 – PQMNRERTGDFS hexagon hexagon

S F

D

GT

R

E

R

N

MQ

P120°

125°100° 10

7(y-55)°

3w+1

P

Find the missing variables

R 55y 120

y 175

RN FD

13w 10

w3 9w 3

HW – p. 282 #1-19 odd, p. 289 #1-9, 12-15

Out – How can you use the names of congruent polygons to determine the congruent sides?

Summary – I have a question about…

POW!!