How do you prove opposite sides are congruent?
Table of Contents
- 1 How do you prove opposite sides are congruent?
- 2 What do you call the segment that is connected to the midpoints of the sides of a triangle or any quadrilateral?
- 3 How do you prove the properties of a parallelogram?
- 4 How do you prove opposite sides of a rectangle are parallel?
- 5 What is mid point theorem in parallelogram?
- 6 How to prove a line segment is parallel to a triangle?
- 7 How to show that the line segments of a quadrilateral bisect each other?
How do you prove opposite sides are congruent?
1. Opposite Sides Theorem Converse: If both pairs of opposite sides of a quadrilateral are congruent, then the figure is a parallelogram. 2. Opposite Angles Theorem Converse: If both pairs of opposite angles of a quadrilateral are congruent, then the figure is a parallelogram.
What do you call the segment that is connected to the midpoints of the sides of a triangle or any quadrilateral?
Midsegment Theorem
Midsegment Theorem. A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
What is the line joining opposite vertices of a polygon called?
diagonal
A diagonal is a straight line connecting the opposite corners of a polygon through its vertex.
How do you prove the properties of a parallelogram?
Well, we must show one of the six basic properties of parallelograms to be true!
- Both pairs of opposite sides are parallel.
- Both pairs of opposite sides are congruent.
- Both pairs of opposite angles are congruent.
- Diagonals bisect each other.
- One angle is supplementary to both consecutive angles (same-side interior)
How do you prove opposite sides of a rectangle are parallel?
Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so: Its opposite sides are equal and parallel.
How do you prove opposite angles are equal?
Given two lines AB and CD intersect each other at the point O. To prove: ∠1 = ∠3 and ∠2 = ∠4 Proof: From the figure, ∠1 + ∠2 = 180° [Linear pair] → (1) ∠2 + ∠3 = 180° [Linear pair] → (2) From (1) and (2), we get∠1 + ∠2 = ∠2 + ∠3 ∴ ∠1 = ∠3 Similarly, we can prove ∠2 = ∠4 also.
What is mid point theorem in parallelogram?
In a parallelogram a line segment joining mid points is parallel to the side. All the three plane figures with this concept is called’ mid point theorem’. Moreover, in parallelogram line segment joining mid points i.e equi.distance, obviously it is parallel to parallel sides.
How to prove a line segment is parallel to a triangle?
If midpoints of any of the sides of a triangle are adjoined by the line segment, then the line segment is said to be in parallel to all the remaining sides and also will measure about half of the remaining sides. Let E and D be the midpoints of the sides AC and AB.
What divides a parallelogram into two equal parallelograms?
Show that line segment joining the mid points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms. Quadrilateral ABCD is a parallelogram. Similarly, quadrilateral EBCF is also a parallelogram. AEFD and EBCF are two parallelograms on the same base EF and between the same parallels, AD and BC.
How to show that the line segments of a quadrilateral bisect each other?
>> Show that the line segments… Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. Line segments joining the mid-points of two sides of a triangle is parallel to the third side and is half of of it.