1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alika [10]
2 years ago
11

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Mathematics
1 answer:
Harlamova29_29 [7]2 years ago
4 0

Answer:

Given: In parallelogram ABCD, AC=BD

To prove : Parallelogram ABCD  is rectangle.

Proof : in △ACB and △BDA

AC=BD  ∣ Given

AB=BA ∣ Common

BC=AD ∣ Opposite sides of the parallelogram ABCD

△ACB ≅△BDA∣SSS Rule

∴∠ABC=∠BAD...(1) CPCT

Again AD ∥ ∣ Opposite sides of parallelogram ABCD

AD ∥BC and the traversal AB intersects them.

∴∠BAD+∠ABC=180∘ ...(2) _ Sum of consecutive interior angles on the same side of the transversal is 

180∘

From (1) and (2) ,

∠BAD=∠ABC=90∘

∴∠A=90∘ and ∠C=90∘

Parallelogram ABCD is a rectangle.

You might be interested in
you are having a garage sale. At Lowe's, a cash box cost $10 and for sale signs cost $7 each. You spent a total of $38 before ta
Crank

Answer:

4 sales signs

Step-by-step explanation:

7x + 10 = 38

<em>Subtract 10</em>

7x = 28

<em>Divide 4</em>

x = 4


6 0
3 years ago
Read 2 more answers
A rectangle has a length of 42 inches and a width of 14 inches. Which of the following is not equal to the ratio of the rectangl
Temka [501]
The ratio of the rectangle's length to its width is 42/14 which simplifies to 3/1 by factoring out 14 out of the numerator and denominator.
Any ratio that is not 3:1, or a multiple of 3:1, is not equal.

List of Equal Ratios: 6:2, 9:3, 12:4, etc.
4 0
3 years ago
What happens to the median of the data set
a_sh-v [17]
Answer: C

Explanation:
5 0
3 years ago
- 7 ( x - 2 ) + 1 = 15 - 7x
Savatey [412]

Answer: x=1

Step-by-step explanation:

You need to open up the parenthesis so you multiply every term inside the parenthesis by -7.

1.  -7x + 14 + 1 = 15 -7x

2. Combine like terms -7x + 15 = 15-7x

The two sides of the equation are the same so that means that x=1

5 0
3 years ago
11 12 13 Please help! Will reward brainliest
RoseWind [281]
11. 9/20
12. 13/20
13. 12/20

that's if it doesn't have to be in percentage form
3 0
3 years ago
Other questions:
  • What is 8 3/4% expressed as a fraction? A.8100 B.780 C.740 D.825
    7·2 answers
  • Consider the rectangular prism with length 3 cm, width 4 cm, and height of 6 cm. Will doubling one of the dimensions of the rect
    8·1 answer
  • A bicycle wheel has a circumference of 62 inches. Find the diameter of the wheel. If necessary, round to the tenths place. 39.5
    8·2 answers
  • Y’all plz help fast
    11·1 answer
  • If y= -4x + 11 and 3x +y= 9, what is the value of y?
    5·1 answer
  • The Department of Education wishes to estimate the proportion of all college students who have a job off-campus. It surveyed 160
    6·1 answer
  • Please help!!!!<br><br>(Division with 2-digit divisors
    8·1 answer
  • HELP PLS ASAP:)<br><br> What is the slope of the line plotted below?<br> A. -1 B. 1 C. -0.5 D. 0.5
    14·2 answers
  • Dont mind this i just need the achivement
    14·2 answers
  • Convert 40 ounces into pounds. Round your answer to the nearest tenth.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!