unit 3 longest-shortest sides

Relationships of angles and sides To order the measures of the sides and angles of a triangle. To use triangle inequalities to solve problems.

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Relationships of angles and sides

To order the measures of the sides and angles of a triangle.

To use triangle inequalities to solve problems.

Theorem

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

Theorem

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Cut segments of one straw into 3, 5, and 9 centimeters.

Can you make a triangle?

Cut segments of one straw into 3, 5, and 9 centimeters.

Can you make a triangle?

StrawsStraws

StrawsStraws

Cut segments of one straw into 4, 5, and 7 centimeters.

Can you make a triangle?

Cut segments of one straw into 4, 5, and 7 centimeters.

Can you make a triangle?

Triangle Inequality Theorem

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

Which segment is shortest?

RORO

Which segment is shortest?

AYAY

Find x. Which side is longest?

X = 59X = 59PEPE

X =10X =10 D D

The perimeter is 51. Find x. Which angle is the smallest?

X =2X =2AA

The perimeter is 22. Find x. Which angle is the largest?

PKPK

Which side is opposite A in APK?

Which angle is opposite AK in APK?

Which side is opposite R in QKR?

QKQK

Which angle is opposite KR in QKR?

Q Q

The side opposite 1 in BKN is _____?

KNKN

The side opposite 1 in BJN is _____?

JNJN

The angle opposite NJ in JNY is _____?

6 orY

__<X<____<X<__

What is the shortest, longest side ED can be?

13 43

__<X<____<X<__

What is the shortest, longest side ED can be?

10 14

What is the shortest, longest side PA can be?

__<X<____<X<__

32 8

X 24 40

What is the shortest, longest side PA can be?

__<X<____<X<__

29 13

X 16 42

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unit 3 longest-shortest sides

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