Opposite sides of a parallelogram
Asked by maham237 @ in Mathematics viewed by 280 People
Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures.
Answered by maham237 @
Theorem : Opposite sides of a parallelogram are congruent or equal.
Let us suppose a parallelogram ABCD.
Given: and
(According to the definition of parallelogram)
We have to prove that: AB is congruent to CD and BC is congruent to AD.
Prove: let us take two triangles, and
In these two triangles, { By the definition of alternative interior angles}
Similarly,
And, AC=AC (common segment)
By ASA,
thus By the property of congruent triangle, we can say that corresponding sides of are also congruent.
Thus, AB is congruent to CD and BC is congruent to AD.
Similar Questions
Prove that opposite sides of a parallelogram are equal
Asked by admin @ in Math viewed by 307 persons
Prove that in a parallelogram opposite sides are equal
Prove that in a parallelogram opposite sides are equal
Asked by admin @ in Math viewed by 321 persons
Prove that in a parallelogram opposite sides are equal
Angle opposite to the side lm of triangle lmn
Asked by admin @ in Math viewed by 396 persons
Write the angle opposite to the side LM of triangle LMN
If all sides of a parallelogram touch a circle
Asked by admin @ in Math viewed by 293 persons
If all the sides of a parallelogram touch a circle show that parallelogram is a rhombus
A parallelogram with a pair of adjacent sides equal
Asked by admin @ in Math viewed by 319 persons
A parallelogram in which a pair of adjacent sides are equal is called a
Prove that opposite angles of a parallelogram are equal
Asked by admin @ in Math viewed by 346 persons
Theorem in a parallelogram opposite angles are equal
A parallelogram whose all sides are equal is called
Asked by admin @ in Math viewed by 369 persons
21. A parallelogram whose all sides are equal is called
(a)square (b)rhombus (c)rectangle (d) trapezium
Prove that in a parallelogram opposite angles are equal
Asked by admin @ in Math viewed by 295 persons
Theorem in a parallelogram opposite angles are equal
Two consecutive sides of a parallelogram are 4x 5y 0
Asked by admin @ in Math viewed by 337 persons
two consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y+0 the equation of one diagonal is 11x+7y-9=0 find the equation of other diagonal.
The opposite sides of a dice always add up to
Asked by admin @ in Math viewed by 320 persons
What is the addition number of opposite sides of a dice which would be the sum of every opposite number in the dice
no googling
The adjacent sides of a parallelogram abcd measure 34 cm
Asked by admin @ in Math viewed by 303 persons
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
In a triangle angle opposite to the longer side is
Asked by admin @ in Math viewed by 325 persons
In a triangle the angle opposite to the longer side is?
What is the length of side ab of parallelogram abcd
Asked by admin @ in Math viewed by 315 persons
What is the length of side AB of parallelogram ABCD? units?
In a triangle the side opposite to greater angle is
Asked by maham237 @ in Mathematics viewed by 389 persons
Which triangle correctly shows that the side opposite the larger angle is the larger side?
The length of the side opposite measures units.
Asked by maham237 @ in Mathematics viewed by 295 persons
The length of the side opposite B measures __ units
Most viewed questions in Mathematics
Unit 6 similar triangles homework 2 similar figures answer key
Asked by maham237 @ in Mathematics viewed by 18362 persons
All things algebra unit 7 polygons and quadrilaterals answer key
Asked by admin @ in Mathematics viewed by 8161 persons
Gina wilson all things algebra 2016 answer key unit 11
Asked by admin @ in Mathematics viewed by 5784 persons
Unit 1 geometry basics homework 4 angle addition postulate answers
Asked by maham237 @ in Mathematics viewed by 3936 persons
Unit 6 exponents and exponential functions homework 8 answer key
Asked by maham237 @ in Mathematics viewed by 3254 persons
The manager of a vacation resort believes that the ages
Asked by maham237 @ in Mathematics viewed by 2925 persons
What is 271 403 rounded to the nearest ten thousand
Asked by maham237 @ in Mathematics viewed by 2798 persons
Unit 1 geometry basics homework 3 angle relationships answer key
Asked by maham237 @ in Mathematics viewed by 2584 persons
Why would a prism beat a sphere in a competition?
Asked by maham237 @ in Mathematics viewed by 2481 persons
An artist sells a painting for 20.50 but uses 5.75
Asked by maham237 @ in Mathematics viewed by 2431 persons
Unit 4 congruent triangles homework 1 classifying triangles answer key
Asked by maham237 @ in Mathematics viewed by 2420 persons
Unit 4 congruent triangles homework 2 angles of triangles
Asked by maham237 @ in Mathematics viewed by 2076 persons
Compare the values of the 2s and 5s in 55220
Asked by maham237 @ in Mathematics viewed by 1794 persons