Triangles Unit Test 92%

If triangle RST is an acute triangle, then m∠S must be

less than 90°.

Which angle is an adjacent interior angle to ∠JKM?

∠MKL

Consider triangle WXY. Which statement about the angles is true?

Angle W is greater than angle Y.

In the triangles, BC = DE and AC = FE. If the mC is greater than the mE, then AB is _________ DF.

longer than

A centroid is the intersection of three

medians in a triangle

In triangle TRS, VZ = 6 inches. What is RZ?

12 inches

In which figure is point G a centroid?

A

What is the value of x?

x = 22

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

m∠A + m∠B = 155°

Point Z is the incenter of ΔSRT. What is mZTB?

31°

Triangle KNM is shown. What is true about the sides of KNM?

KN = NM

Point Z is the circumcenter of ΔLMN. Which must be true?

ZBM = ZCM

Triangle JKL is isosceles. The measure of angle J is 72° and the measure of angle K is 36°. Which statement describes angle L?

Angle L is a base angle and measures 72°.

Triangle XYZ is isosceles. Angle Y measures a°. What expression represents the measure of angle X?

180 - 2a

Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle?

8 cm and 8 cm

In the diagram, which must be true for point D to be an orthocenter?

BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB.

Based on the diagram, which expresses all possible lengths of segment AB?

27 < AB < 81

What is the m∠ABC?

m∠ABC = 60°

The lengths of the sides of triangle XYZ are in terms of the variable m, where m ≥ 6. Which is correct regarding the angles of the triangle?

mY < mZ < mX

Which statements regarding the diagram of ΔEBC are true? Check all that apply.

∠DEC is an exterior angle. ∠ABE and ∠EBC are supplementary angles. ∠BEC is a remote interior angle to exterior ∠BCF.

Point H is the circumcenter of triangle DEF. Which must be true? Check all that apply.

Point H is the center of the circle that passes through points D, E, and F. HE = HD LH = NH

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles?

54°

What is the length of segment NS?

4 units

Point X is the circumcenter of ΔABC. What is the length of XB?

5.3 cm

Nigel and Mia are searching for a treasure chest under water. The straight line distance between them is 100 meters. Given the angles in the diagram, who is closer to the treasure chest and why?

Mia is closer because her distance to the chest is opposite the smaller angle.