Cumulative Assessment H6

Line GH is tangent to ⊙T at N. If m∠ANG = 54, what is measure of arc AB?

• 72

• 54

• 36

• 108

Point Q lies on the angle bisector of ∠BAC and is 4 units from AB How many units is point Q from AC?

• 8

• 2

• 1

• 4

The area of a rhombus is pq/2, where p and q are the length of each diagonal. A rhombus has an area of 600 square units and a perimeter of 100 units. How long is each side, and each of the diagonals?

• side length: 20, diagonals: 22 and 40

• side length: 25, diagonals: 26 and 36

• side length: 20, diagonals: 26 and 48

• side length: 25, diagonals: 30 and 40

What is the value of x? Round your answer to two decimal places if needed.

• 5.74

• 3.21

• 6.89

• 4.56

If you are given the coordinates of A, B, C, and D, select all the ways that you could prove that ABCD is a rectangle.

• Use the slope formula to show that AB ∥ CD, BC ∥ AD, and AC ⟂ BD.

• Use the distance formula to show that AB = CD and BC = AD, and use the midpoint formula to show that the midpoint of AC and the midpoint of BD are the same point.

• Use the distance formula to show that AB = CD and BC = AD, and use the midpoint formula to show that the midpoint of AC and the midpoint of BD are the same point.

• Use the distance formula to show that AB = CD, and use the slope formula to show that AB ∥ CD and AB ⟂ BC.

• Use the slope formula to show that AB ∥ CD, and use the distance formula to show that AB = CD and AC = BD.

What is the value of x?

(a)  

In △TJB and △DSP, JB ≅ SP and ∠B ≅ ∠P. Which additional piece(s) of information is needed to prove that the triangles are congruent by each given theorem?

ASA​ (a)  

SSS ​ (b)   ​ (c)  

SAS ​ (d)  

AAS​ ​ ​ (e)  

If a pyramid intersects a plane that is parallel to its base, what must be true about the cross section?

• The cross section is a square.

• The cross section is a triangle.

• The cross section is similar to the base.

• The cross section is congruent to the base.

Jack’s eyes are 5 feet above the ground. He is standing 400 feet from the base of a building. The angle of elevation of his line of sight to the top of the building is 67°. About how tall is the building?

• 161 ft

• 175 ft

• 373 ft

• 947 ft

Which point is the center of the circle that contains the vertices of a triangle?

• the point of intersection of the altitudes

• the point of intersection of the perpendicular bisectors of the sides

• the point of intersection of the angle bisectors

• the point of intersection of the medians