5 6 inequalities involving 2 triangles
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5-6: Inequalities Involving 2 Triangles. Expectation: G1.2.2 Construct and justify arguments and solve problems involving angle measure, side length, perimeter and area of all types of triangles. In the triangles below, 2 pairs of corresponding sides are congruent. Compare the third sides. x.

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5-6: Inequalities Involving 2 Triangles

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5 6 inequalities involving 2 triangles

5-6: Inequalities Involving 2 Triangles

  • Expectation:

  • G1.2.2 Construct and justify arguments and solve problems involving angle measure, side length, perimeter and area of all types of triangles.


In the triangles below 2 pairs of corresponding sides are congruent compare the third sides

In the triangles below, 2 pairs of corresponding sides are congruent. Compare the third sides.

x

2.17

2.17

y

82°

32°

2.67

2.67


Sas inequality hinge theorem

SAS Inequality (Hinge Theorem)

  • If two sides of one triangle are congruent to 2 sides of a second triangle, but the included angle of the first is greater than the included angle of the second, then the 3rd side of the first is _______________ than the 3rd side of the second.


5 6 inequalities involving 2 triangles

Two pairs of corresponding sides are congruent in the triangles below. Compare the included angles for the given congruent sides.


Sss inequality

SSS Inequality

  • If two sides of one triangle are congruent to 2 sides of a second triangle, but the third side of the first is longer than the third side of the second, then the included angle between the pair of congruent sides of the first is ______________ than the included angle between the pair of congruent sides of the second.


Use the figure to compare the indicated measures

Use the figure to compare the indicated measures.

E

8

D

10

10

9

6

C

8

A

B

9

a. m∠ADB and m∠DBC


Use the figure to compare the indicated measures1

Use the figure to compare the indicated measures.

E

8

D

10

10

9

6

C

8

A

B

9

b. m∠EAD and m∠BCD


5 6 inequalities involving 2 triangles

In ΔABC and ΔDEF below (not drawn to scale) AB, BC, DE and EF are all 12 units long. If m∠A = 30° and m∠F = 50°, compare AC and DF.

B

E

  • AC = DF

  • AC > DF

  • AC < DF

  • not enough information given to determine an answer.

A

D

C

F


5 6 inequalities involving 2 triangles

Given : QC bisects PD and m∠PCQ > m∠DCQ

Prove: m∠D > m∠P

P

C

D

Q


5 6 inequalities involving 2 triangles

Assignment:

pages 277,

# 15 - 29 (odds)


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