# Geometry Postulates and Theorems

### 33 terms by melodykearney

#### Study  only

Flashcards Flashcards

Scatter Scatter

Scatter Scatter

## Create a new folder

If point B is on segment AC and between points A and C, then AB + BC = AC

### Vertical Angles Theorem

If two angles are vertical angles, then the angles are congruent.

### Linear Pair Theorem

If two angles form a linear pair, then the measures of the angles add up to 180°.

If point D is in the interior of <ABC, then m< ABD + m< DBC = m< ABC

### Parallel Postulate

If there is a line and point not on the line, then there is one and only one line through the point parallel to the given line.

### Perpendicular Postulate

If there is a line and a point not on the line, then there is one and only one line through the point perpendicular to the given line.

### Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

### Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

### Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

### Same-side Interior Angles Theorem

If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

### Same-side Exterior Angles Theorem

If two parallel lines are cut by a transversal, then same-side exterior angles are supplementary.

### Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.

### Shortest Distance Theorem

The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.

### Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

### Triangle Sum Theorem

The sum of the measures of the angles in every triangle is 180°.

### Isosceles Triangle Theorem

If a triangle is isosceles, then its base angles are congruent.

### Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

### Triangle Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

### Polygon Sum Theorem

The sum of the measures of the n interior angles of an n-gon is 180°(n - 2).

### Exterior Angle Sum Theorem

The sum of the measures of a set of the exterior angles of a polygon is 360°.

### Trapezoid Midsegment Theorem

A midsegment of a trapezoid is parallel to the bases and equal to the average of the bases.

### Angle-Angle Similarity Theorem (AA)

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

### Side-Side-Side Similarity Theorem (SSS)

If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are similar.

### Side-Angle-Side Theorem (SAS)

If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

### Dilation Similarity Theorem

If one polygon is a dilated image of another polygon, then the polygons are similar.

### Side-Splitter Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides proportionally.

### Altitude of a Right Triangle Theorems

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle AND The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

### Perimeter of Similar Polygons Theorem

If two polygons are similar, then the ratio of their perimeters is equal to the ratio of any pair of corresponding sides.

### Area of Similar Polygons Theorem

If two polygons are similar, then the ratio of their areas is equal to the ratio of the squares of the lengths of any pair of corresponding sides.

### Circumference Theorem

If C is the circumference and d is the diameter of a circle, then there is a number (pi) such that C=(pi)d. If d=2r where r is the radius, then C= 2r(pi)

### Tangent Theorem

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

### Tangent Segment Theorem

Tangent segments to a circle from a point outside the circle are congruent.

### Inscribed Angle Theorem

The measure of an angle inscribed in a circle is half the measure of its intercepted arc.

Example: