Triangle Properties

Triangle Properties

by David Miller

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​2 congruent sides

​no equal sides all angles acute 1 obtuse, 2 acute angles

​all sides &

angles equal

​1 right angles,

2 acute angles

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Multiple Select

Under which angle conditions could a triangle exist? Check all that apply

• 3 acute angles

• 2 acute angles, 1 right angle

• 1 acute angle, 1 right angle, 1 obtuse angle

• 1 acute angle, 2 obtuse angles

• 2 acute angles, 1 obtuse angles

Multiple Choice

Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be

• less than 90°.

• greater than 90°.

• congruent to angle B.

• congruent to angle C.

Multiple Select

If triangle DEF has a 90° angle at vertex E, which statements are true? Select two options.

• Triangle DEF is an obtuse triangle.

• The angle at vertex D is acute.

• The angle at vertex F is obtuse.

• Triangle DEF is a right triangle.

• The angle at vertex D is obtuse

Multiple Choice

If the longest side of the triangle was 10. Then the two shorter sides must have a sum that is ....?

• any length

• equal to 10

• greater than 10

• less than 10

Multiple Choice

Can the sides of a triangle have lengths 3, 4, and 9?

• Yes

• No

• I don't know

• Cannot be determined

Fill in the Blanks

Multiple Choice

Triangle DEF contains two congruent acute angles. The sum of the measures of the two congruent acute angles is greater than 90 degrees. Anna concludes that the triangle must be an acute triangle. Which best describes her conclusion?

• She is correct. A triangle having at least one acute angle is an acute triangle.

• She is correct. The remaining angle of the triangle measures less than 90 degrees.

• She is incorrect. The angles measure greater than 90 degrees so the triangle is obtuse.

• She is incorrect. The third angle in a triangle with two congruent acute angles is a right angle.

Multiple Choice

Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

• AC + AB > CB

• AC + CB < AB

• AC + CB > AB

• AC + AB < CB

Multiple Choice

A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n?

• 5 < n < 15

• 5 < n < 20

• 15 < n < 20

• 15 < n < 25

Multiple Choice

Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true?

• This triangle exists because the sum of any two side lengths is greater than the length of the third side.

• This triangle exists because the sum of 4 and 12 is less than 17.

• This triangle does not exist because the sum of any two side lengths is greater than the length of the third side

• This triangle does not exist because the sum of 4 and 12 is less than 17.

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Multiple Choice

Which triangle correctly shows that the side opposite the larger angle is the larger side?

Multiple Choice

Pat is at a right angle from Chris and Jaime, and Chris is at a 48° angle from Pat and Jaime. Which statements are true? Check all that apply.

• Jaime is at the smallest angle from the two friends.

• Pat is at an angle of 90° to Chris and Jaime.

• The path between Jaime and Chris is the shortest because it is adjacent to the smallest angles.

• If they meet at Pat’s entrance, then Chris will have walked a shorter distance than Jaime. 

• If they meet at Jaime’s entrance, then Pat will have walked a longer distance than Chris.

Multiple Choice

Which statement is true regarding triangle TUV?

• Angle T is the smallest angle

• Angle V is the smallest angle

• Angle U and V must be equal

• Angles U & T must be equal

Multiple Choice

Which shows the order of the angles from smallest to largest?

• angle A, angle B, angle C

• angle B, angle A, angle C

• angle B, angle C, angle A

• angle C, angle A, angle B

Multiple Choice

Hint: draw out the image described

Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she  travels 5 miles to return home. The entire trip forms a triangle. What is the smallest angle made in her trip?

• It is at the gas station.

• It is at Lucy’s home.

• It is at the post office.

• It depends on the direction Lucy is traveling.

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Multiple Choice

Given AC = LN and BA = ML, which statement must be true?

• BC < MN

• BC > MN 

• BC = MN

• BA = LN

Multiple Choice

Given GK = XZ and GH = XY, which statement must be true?

• m∠G > m∠X

• m∠G < m∠X

• HG = XZ

• HK = YZ

Multiple Choice

A fence runs along the back wall of each property, as shown in the diagram.

Which lot has the longest fence along the back wall?

• lot 1

• lot 2

• lot 3