An isosceles trapezoid has the following unique properties: One pair of parallel sides. Base angles are congruent. The legs are congruent.
What makes a trapezoid an isosceles trapezoid?
A trapezoid is a quadrilateral with exactly one pair of parallel sides. A pair of angles that share a base as a common side are called a pair of base angles. A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.
How many properties does an isosceles trapezoid have?
Isosceles trapezoids have two sides that are opposite and parallel. The angles adjacent to each non-parallel side are supplementary. The angles adjacent to each parallel side are congruent. The non-parallel sides have the same length.
What is the difference between a trapezoid and an isosceles trapezoid?
A trapezoid is a quadrilateral where one pair of sides is parallel while the other two sides are not. In an isosceles trapezoid the non-parallel sides are congruent.
Is a trapezoid always isosceles?
An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent. Theorem: The base angles of an isosceles trapezoid are congruent. The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.
How do you prove an isosceles trapezoid?
One way to prove that a quadrilateral is an isosceles trapezoid is to show:
The quadrilateral has two parallel sides.
The lower base angles are congruent and the upper base angles are congruent.
Which best describes the diagonals of an isosceles trapezoid?
Diagonals are congruent.
What is the greatest number of right angles an isosceles trapezoid may have?
Explanation: A trapezoid can have either 2 right angles, or no right angles at all.
How do you prove parallel lines?
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. If two lines are parallel to the same line, then they are parallel to each other.
What are five ways to prove two lines are parallel?
Ways to Prove Two Lines Parallel
Show that corresponding angles are equal.
Show that alternative interior angles are equal.
Show that consecutive interior angles are supplementary.
Show that consecutive exterior angles are supplementary.
In a plane, show that the lines are perpendicular to the same line.
What is the parallel lines theorem?
If two corresponding angles are congruent, then the two lines cut by the transversal must be parallel. Similarly, if two alternate interior or alternate exterior angles are congruent, the lines are parallel.
What are two parallel lines cut by a transversal?
If two parallel lines are cut by a transversal, then, Alternate Exterior Angles are congruent. If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
What happens when a transversal crosses parallel lines?
First, if a transversal intersects two parallel lines, then the alternate interior angles are congruent. The proposition continues by stating that on a transversal of two parallel lines, corresponding angles are congruent and the interior angles on the same side are equal to two right angles.
What happens when a transversal intersects two parallel lines?
As per the theorem, when a transversal intersects two parallel lines, each pair of alternate interior angles are equal. Conversely, if a transversal intersects two lines such that a pair of interior angles are equal, then the two lines are parallel.
What 3 things happen when parallel lines are cut by a transversal?
Corresponding Angles are congruent. Alternate Exterior Angles are congruent. Alternate Interior Angles are congruent. Same Side Interior Angles (Consecutive Interior Angles) sum to 180 degrees.
What is the best example of pair of lines that are parallel?
However, these two lines L and M, lying in the same plane are parallel if they do not meet anywhere, however far they are extended. Note that the distance between two parallel lines is the same everywhere. For example a railway track, opposite sides of a blackboard, two opposite edges of a door etc.
Which are the parallel lines?
In geometry, parallel lines are lines in a plane which do not meet; that is, two straight lines in a plane that do not intersect at any point are said to be parallel. A line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are also said to be parallel.
Which line in Figure 1 is a transversal line?
For two or more straight lines, a transversal is any line that intersects two straight lines at distinct points. In the following figure, L1 and L2 are two lines that a transversal L cuts. Here, the L line is known as the transverse line.
What are the main parts of a parallel line?
Parallel lines are lines in the same plane that do not intersect. Line segments and rays that are parts of parallel lines are also parallel.
How do you solve a transversal line?
What are the angles between the two parallel lines?
Answer. Answer: the angle between parallel lines is undefined, or it can be either 0 or 180 degrees, or any multiple of 180 degrees.