Team Quiz : Reviewing Geo MCA Concepts

Write the Converse of:

If a polygon has 4 sides, then it is a quadrilateral.

• If a polygon is not a quad, then it does not have 4 sides.

• If a polygon is a quad, then it has 4 sides.

• If a polygon does not have 4 sides, then it is a quad.

• If a polygon does not have 4 sides, then it is not a quad.

Answer explanation

The correct choice states that if a polygon is a quadrilateral, then it must have 4 sides, which is the converse of the given statement.

What is the perimeter of square ABCD?

• 5

• 20sqrt(2)

• 20

• 10

Answer explanation

1. 1. Diagonal is 5*Sqrt(2).
   2. See 45-45-90 triangles.
   3. Note that the sides must be 5.

2. 4. 5*4 = 20

Calculate the value of x using similar triangles or a theorem we've learned.

• x = 33

• x = sqrt(33)

• x = 11/3

• x = 3/11

Answer explanation

1.) Similar triangles --> 3/x = x/11

leads to x^2 = 33 --> x = sqrt(33)

2.) Alt^2 = Part1 * Part2 -->

x = sqrt(33)

Use Isosceles Triangle Facts!

• x = 26

• x = 29

• x = 58

• x = 116

Answer explanation

1.) Triangle on right --> base angles congruent means 58 degrees each.

2.) Then find vertex angle of left angle.

3.) Then find base angles of left triangle.

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°.
How tall is the building?

• 373 ft

• 175 ft

• 947 ft

• 161 ft

Answer explanation

1.) Tangent appropriate here.
2.) Don't forget to account for the boy's height!

Points A, B, and C are collinear and B is between A and C. You are given AC = 18 and BC = 4. What is the value of AB?

• AB = 22

• AB = 14

• AB = 20

• AB = 12

Answer explanation

Draw a picture!

What is the length of segment AD if A = (5,2) and D = (-3, -4)

• 10

• 36

Answer explanation

Length of a segment and distance formula are interchangeable ideas.

• DF = 8

• DF = 3

• DF = 5

• DF = 11

Answer explanation

Isosceles trapezoid --> diagonals are congruent!