Triangle Properties

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

less than 90°.

greater than 90°.

congruent to angle B.

congruent to angle C.

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

any length

equal to 10

greater than 10

less than 10

Yes

No

I don't know

Cannot be determined

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.

AC + AB > CB

AC + CB < AB

AC + CB > AB

AC + AB < CB

5 < n < 15

5 < n < 20

15 < n < 20

15 < n < 25

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.

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.

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

angle A, angle B, angle C

angle B, angle A, angle C

angle B, angle C, angle A

angle C, angle A, angle B

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.

BC < MN

BC > MN 

BC = MN

BA = LN

m∠G > m∠X

m∠G < m∠X

HG = XZ

HK = YZ

lot 1

lot 2

lot 3