Geometry Chapter 5 Test

1) In the diagram given, which angle has the greatest measure of

angle 1 comma space angle 3 comma space angle 4

.

$angle 1$
$angle 3$
$angle 4$
cannot be determined

A

B

C

D

Without any additional information or measurements provided in the diagram, it is not possible to determine which angle has the greatest measure. Therefore, the correct answer is "cannot be determined".

Explanation

Without any additional information or measurements provided in the diagram, it is not possible to determine which angle has the greatest measure. Therefore, the correct answer is "cannot be determined".

2) Which set of numbers cannot represent the lengths of the sides of a triangle?

6, 8, 11

5, 6, 7

7, 11, 18

9, 12, 19

In order for a set of numbers to represent the lengths of the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In the given set, the sum of the lengths of the two smaller sides (7 and 11) is equal to the length of the longest side (18), violating the triangle inequality theorem. Therefore, the set 7, 11, 18 cannot represent the lengths of the sides of a triangle.

Explanation

In order for a set of numbers to represent the lengths of the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In the given set, the sum of the lengths of the two smaller sides (7 and 11) is equal to the length of the longest side (18), violating the triangle inequality theorem. Therefore, the set 7, 11, 18 cannot represent the lengths of the sides of a triangle.

3) Determine the relationship between

stack D H with bar on top comma space stack G H with bar on top

DH = GH

DH < GH

DH > GH

No relationship

The given answer states that DH is greater than GH. This implies that DH is larger or has a higher value than GH.

Explanation

The given answer states that DH is greater than GH. This implies that DH is larger or has a higher value than GH.

4) The point of concurrency of the medians of a triangle and is two thirds of the distance form each vertex to the midpoint of the opposite side.

Centroid

Incenter

Orthocenter

Circumcenter

Nine-Point Center

The centroid of a triangle is the point of concurrency of the medians. A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The centroid is located two thirds of the distance from each vertex to the midpoint of the opposite side. Therefore, the correct answer is centroid.

Explanation

The centroid of a triangle is the point of concurrency of the medians. A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The centroid is located two thirds of the distance from each vertex to the midpoint of the opposite side. Therefore, the correct answer is centroid.

5) The point of concurrency of the perpendicular bisectors of a triangle and is equidistant from the vertices of a triangle.

Centroid

Incenter

Orthocenter

Circumcenter

Nine-Point Center

The circumcenter is the point of concurrency of the perpendicular bisectors of a triangle. It is equidistant from the vertices of the triangle, meaning that the distance from the circumcenter to each vertex is the same. This property makes the circumcenter the center of the circumcircle, which is a circle that passes through all three vertices of the triangle.

Explanation

The circumcenter is the point of concurrency of the perpendicular bisectors of a triangle. It is equidistant from the vertices of the triangle, meaning that the distance from the circumcenter to each vertex is the same. This property makes the circumcenter the center of the circumcircle, which is a circle that passes through all three vertices of the triangle.

6) The point of concurrency of the angle bisectors of triangle and is equidistant from the sides of a triangle.

Centroid

Incenter

Orthocenter

Circumcenter

Nine-Point Center

The incenter of a triangle is the point of concurrency of the angle bisectors. It is the center of the inscribed circle, which is equidistant from all three sides of the triangle. Therefore, the given statement is true and the correct answer is "Incenter".

Explanation

The incenter of a triangle is the point of concurrency of the angle bisectors. It is the center of the inscribed circle, which is equidistant from all three sides of the triangle. Therefore, the given statement is true and the correct answer is "Incenter".