Question 1

-Where M, N, and P are the midpoints of the sides of  and C is the centroid of the triangle, it follows that  .

Accepted Answer

The answer of 
-Where M, N, and P are the...

Question 2

-To construct the altitude from vertex A to side  of the obtuse triangle  , one begins by constructing the midpoint of  .

Accepted Answer

The answer of 
-To construct the altitude from vertex A...

Question 3

Consider  in which m  = 90°. Find the point at which the three altitudes are concurrent.

Accepted Answer

The answer of Consider  in which m  =...

Question 4

What is the name of the point at which the three angle-bisectors of the angles of a triangle are concurrent?

Accepted Answer

The answer of What is the name of the point...

Question 5

-In equilateral triangle  , the orthocenter is point O. If XY = 18 mm, find the distance from point O to any side of  .

Accepted Answer

The answer of 
-In equilateral triangle  , the orthocenter...

Question 6

What is the locus of points that are at distance 3 cm from the sphere with center S and whose length of radius is 3 cm.?

Accepted Answer

The answer of What is the locus of points that...

Question 7

Find the locus of points in space that are equidistant from points A and B.

Accepted Answer

The answer of Find the locus of points in space...

Question 8

-The point at which the three angle-bisectors of the angles of a triangle are concurrent is known as the circumcenter of the triangle.

Accepted Answer

The point at which the three angle-bisectors of the angles of a triangle meet is known as the incenter of the triangle, not the circumcenter. The circumcenter is the point where the perpendicular bisectors of the sides of the triangle meet.

Question 9

What is the locus of points in space that are at a given distance r from line l?

Accepted Answer

The answer of What is the locus of points in...

Question 10

-The three altitudes of an obtuse triangle are concurrent at a point that lies in the exterior of that triangle.

Accepted Answer

In an obtuse triangle, the altitudes (perpendiculars dropped from the vertices to the opposite sides) are concurrent at a point called the orthocenter, which lies outside the triangle for obtuse triangles.

Question 11

In order to determine one point that is equidistant from points A and B, which basic construction can be performed?

Accepted Answer

The answer of In order to determine one point that...

Question 12

-Consider right triangle  with m  = 90°. Construct the circle that has its center at the midpoint M of hypotenuse  and with radius length of MB. Describe the circle that results.

Accepted Answer

The answer of 
-Consider right triangle  with m ...

Question 13

What construction can be performed to find the locus of points equidistant from the sides of  ?

Accepted Answer

The answer of What construction can be performed to find...

Question 14

-For the points X, Y, and Z, how can you locate the point S that is equidistant from all?

Accepted Answer

The answer of 
-For the points X, Y, and Z,...

Question 15

-To construct the square ABCD with the diagonal  as shown, begin by constructing the perpendicular-bisector of  .

Accepted Answer

The answer of 
-To construct the square ABCD with the...

Question 16

-For a triangular piece of cardboard of uniform thickness, what is another name for the centroid?

Accepted Answer

The answer of 
-For a triangular piece of cardboard of...

Question 17

-A number of lines are concurrent if they have exactly one point in common.

Accepted Answer

Concurrent lines are defined as three or more lines in a plane that intersect at a single point.

Question 18

Given hypotenuse  , describe the locus of points in a plane that are the vertices of a right triangle.

Accepted Answer

The answer of Given hypotenuse  , describe the locus...

Question 19

Describe the locus of points in a plane that are equidistant from two intersecting lines l and m.

Accepted Answer

The answer of Describe the locus of points in a...

Question 20

-In a triangle, the lengths of the sides are 9, 12, and 15. What is the length of the radius of the circumcircle?

Accepted Answer

The answer of 
-In a triangle, the lengths of the...

Quiz 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles

-Where M, N, and P are the midpoints of the sides of and C is the centroid of the triangle, it follows that .

-To construct the altitude from vertex A to side of the obtuse triangle , one begins by constructing the midpoint of .

Consider in which m = 90°. Find the point at which the three altitudes are concurrent.