Which of the following statements is the converse of perpendicular bisector theorem?

The converse of the perpendicular bisector theorem states that if a point is equidistant from both the endpoints of the line segment in the same plane, then that point is on the perpendicular bisector of the line segment.

Is the converse of the perpendicular bisector theorem true?

In addition to the Perpendicular Bisector Theorem, the converse is also true. Perpendicular Bisector Theorem Converse: If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

Which of the following statement describes perpendicular bisector theorem?

What is Perpendicular Bisector Theorem? Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

Which statement is the converse of angle bisector theorem?

The angle bisector theorem converse states that if a point is in the interior of an angle and equidistant from the sides, then it lies on the bisector of that angle. The incenter is the point of intersection of the angle bisectors in a triangle.

How do you find the perpendicular bisector theorem?

What is the Converse Perpendicular Bisector Theorem - Congruent Triangles

What is the conclusion of converse of the perpendicular bisector theorem?

The converse of the perpendicular bisector theorem states that if a point is equidistant from both the endpoints of the line segment in the same plane, then that point is on the perpendicular bisector of the line segment.

What is the converse of the hinge Theorem?

The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second ...

What is converse isosceles triangle theorem?

If two angles of a triangle are congruent , then the sides opposite to these angles are congruent.

What is a perpendicular bisector of a triangle?

The perpendicular bisectors of a triangle are lines passing through the midpoint of each side which are perpendicular to the given side. A triangle's three perpendicular bisectors meet (Casey 1888, p. 9) at a point. known as the circumcenter (Durell 1928), which is also the center of the triangle's circumcircle.

What is an example of a perpendicular bisector?

Step 1: A perpendicular bisector divides a line segment into two equal parts. Step 2: The length of AB is 12 cm and CD is the perpendicular bisector of AB.

What are the properties of perpendicular bisectors?

Which of the following theorem can be used to prove that two lines are perpendicular?

Use the diagram to prove the Perpendicular Transversal Theorem. and the Alternate Exterior Angles Theorem (Theorem 3.3). If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

What is the perpendicular transversal theorem?

In a plane, if a line is perpendicular to one of two parallel lines , then it is perpendicular to the other line also.

What is a converse theorem in geometry?

The converse of the Pythagorean Theorem states that if the square of the third side of a triangle is equivalent to the sum of its two shorter sides, then it must be a right triangle.

Is the converse of a theorem always true?

The truth value of the converse of a statement is not always the same as the original statement. For example, the converse of "All tigers are mammals" is "All mammals are tigers." This is certainly not true. The converse of a definition, however, must always be true.

Is the converse of the Isosceles Triangle Theorem true?

The converse of the Isosceles Triangle Theorem is also true. If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

What is the other name for converse of hinge inequality theorem?

The converse of the Hinge Theorem, referred to as the SSS Inequality Theorem, is also true. SSS Inequality Theorem: Consider two triangles, △ABC and △DEF, with ¯¯¯¯¯¯¯¯AB=¯¯¯¯¯¯¯¯¯DE, ¯¯¯¯¯¯¯¯AC=¯¯¯¯¯¯¯¯¯DF, and \overline{EF}. ">¯¯¯¯¯¯¯¯BC>¯¯¯¯¯¯¯¯EF. Then m\angle D.">m∠A>m∠D.

What is Hinge Theorem example?

The Hinge Theorem states that in the triangle where the included angle is larger, the side opposite this angle will be larger. It is also sometimes called the "Alligator Theorem" because you can think of the sides as the (fixed length) jaws of an alligator- the wider it opens its mouth, the bigger the prey it can fit.

What postulate theorem did you use to prove the inequalities in a triangle?

According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side. A polygon bounded by three line-segments is known as the Triangle. It is the smallest possible polygon. A triangle has three sides, three vertices, and three interior angles.

Why do perpendicular bisectors intersect?

It can be concluded then that all three perpendicular bisectors, FD, FE, and FG, are concurrent at point F because point F is equidistant from all three vertices of the triangle. This point is also called the circumcenter because it is the center of the circle that circumscribes the triangle.

How do you prove perpendicular?

If the slopes of two lines can be calculated, an easy way to determine whether they are perpendicular is to multiply their slopes. If the product of the slopes is , then the lines are perpendicular. In this case, the slope of the line is and the slope of the line is .

Which of the following theorems can be used to prove two lines are cut by a transversal?

The answer is D: The Alternate Exterior Angles Converse Theorem. This Alternate Exterior Angles theorem explains that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

How do you prove two lines are perpendicular?

If the two lines intersect at a point, the vertical angles formed are congruent. The intersecting lines either form a pair of acute angles and a pair of obtuse angles, or the intersecting lines form four right angles. When the lines meet to form four right angles, the lines are perpendicular.