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Definitions

100

The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.

TRIANGLE INEQUALITY THEOREM

200

The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle

EXTERIOR ANGLE INEQUALITY THEOREM

300

If two angles of a triangle are not congruent, then the larger side is opposite the larger angle

ANGLE-SIDE INEQUALITY THEOREM

400

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second.

HINGE THEOREM OR SAS INEQUALITY

500

If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second

CONVERSE OF THE HINGE THEOREM OR SSS INEQUALITY

Triangle Inequality

100

Could a triangle have side length as 6cm, 7cm and 5cm?

6 + 7 > 5 ⇒ 13 > 5 ⇒ True

7 + 5 > 6 ⇒ 12 > 6 ⇒ True

6 + 5 > 7 ⇒ 11 > 7 ⇒ True

CAN FORM A TRIANGLE

200

If 4cm, 8cm and 2cm are the measures of three lines segment. Can it be used to draw a triangle?

4 + 8 > 2 ⇒ 12 > 2 ⇒ True

8 + 2 > 4 ⇒ 10 > 4 ⇒ True

4 + 2 > 8 ⇒ 6 > 8 ⇒ False

CANNOT FORM A TRIANGLE

300

TRUE OR FLASE 

Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

True

400

Peter has three measurements with him: 6 cm, 10 cm, and 17 cm. Will he be able to form a triangle with these three measurements?

6 + 10 > 17

⇒ 16 > 17 (false, 17 is not less than 16)

6 + 17 > 10

⇒ 23 > 10 (this is true)

10 + 17 > 6

⇒27 > 6 (this is true)

500

Which of the following is NOT true about the Triangle Inequality Theorem? 

1. AB + BC > AC

2. AB + AC < BC 

3. BC + AC > AB 

2. AB + AC < BC

Random

100

Which is the largest angle?

 A. ∠𝐷 

B. ∠𝑂

C. ∠𝑃

D. Cannot be determined

B. ∠𝑂

200

What is the measure of ∠Y?  

90^° 

300

Which angle has the greatest measure?

∠B

400

What is the largest Angle?

∠E

500

Which is greater? 

m∠1

Arrange the Order

100

. Given below is ∆𝐴𝑅𝑇. List the sides from the longest to the shortest. 

A. 𝐴𝑇̅̅̅̅, 𝐴𝑅̅̅̅̅, 𝑅𝑇̅̅̅̅

B. 𝐴𝑅̅̅̅̅, 𝑇𝑅̅̅̅̅, 𝑇𝐴̅̅̅̅ 

C. 𝑅𝑇̅̅̅̅, 𝑅𝐴̅̅̅̅, 𝑇𝐴̅̅̅̅ 

D. 𝑇𝐴̅̅̅̅, 𝑇𝑅̅̅̅̅, 𝐴𝑅̅̅̅̅

A. 𝐴𝑇̅̅̅̅, 𝐴𝑅̅̅̅̅, 𝑅𝑇̅̅̅̅

500

Arrange the angles of ∆𝐴𝐵𝐶 from greatest to least measure given the lengths of its sides. 

1. |𝐴𝐵| = 5 𝑐𝑚, |𝐵𝐶| = 10 𝑐𝑚, |𝐴𝐶| = 12 𝑐𝑚 

AC,BC,AB