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]
3 years ago
11

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

Mathematics
1 answer:
Harlamova29_29 [7]3 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
Need help on this question
stellarik [79]

Answer:nhjhbghhnkjn hojn

3 0
3 years ago
Read 2 more answers
Write an equation of a line in slope-intercept form given the slope (m) and the y- intercept (b), slope, m= -4/7 y-intercept b =
Leno4ka [110]
The answer is y=-4/7x+7. You simply substitute in the given numbers. -4/7 for the slope (m) and 7 for the y-intercept (b). 
4 0
3 years ago
The cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where X=C/85-12/17 is the number
dybincka [34]

Given:

The cost C (in dollars) to participate in a ski club is given by,

\begin{gathered} C=85x+60 \\ (or) \\ x=\frac{C}{85}-\frac{12}{17} \end{gathered}

Where x is the number of ski trips we take.

To find:

The number of ski trips when a total cost of $315 and $485 is spent.

Explanation:

Substituting C = 315 in the given equation we get,

\begin{gathered} x=\frac{315}{85}-\frac{12}{17} \\ x=\frac{315-60}{85} \\ x=\frac{255}{85} \\ x=3\text{ ski trips} \end{gathered}

Substituting C = 485 in the given equation we get,

\begin{gathered} x=\frac{485}{85}-\frac{12}{17} \\ x=\frac{485-60}{85} \\ x=\frac{425}{85} \\ x=5\text{ ski trips} \end{gathered}

Thus,

If we spend a total cost of $315, we can take 3 ski trips.

If we spend a total cost of $485, we can take 5 ski trips.

Final answer:

• If we spend a total cost of $315, we can take 3 ski trips.

,

• If we spend a total cost of $485, we can take 5 ski trips.

8 0
1 year ago
What is the mean weight ___ pounds ?
natulia [17]
It is 84 ibs
Explanation
It’s actually easy if you learn 5 minutes of it
But thats the correct answer
8 0
3 years ago
If x is 6, then 7x = _____. 13 42 42x 76
Vilka [71]

I can't understand what you wanted with the second question (or if that is even a question), but the answer to the first one is 42.

7 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP IMMEDIATELY!! will MARK BRAINLIEST AND GIVE 16 POINTS! (multiple choice but please try to show steps)
    6·1 answer
  • How many gallons is 32 quarts
    14·2 answers
  • Need so help on all of this
    5·1 answer
  • Given: T is the midpoint of JK¯¯¯¯¯JK¯, JK = 5x – 3, and JT = 2x + 1. Determine the length of JK¯¯¯¯¯JK¯
    6·2 answers
  • What would be the correct answer?
    9·1 answer
  • On Monday, Jill used 12 quart of paint in 34 hour. On Tuesday, Jill was distracted by texting and used 12 quart of paint in 54 h
    12·1 answer
  • What is the value of x??? plzzz help
    6·1 answer
  • Matt Kaminsky bought a Volvo that is 33∕4 times as expensive as the car his parents bought. If his parents paid $8,000 for their
    8·2 answers
  • Help!!!!!(ToT) thnaks
    7·1 answer
  • icating any part of this book is prohibited by law. Solve. 18. EXPLAIN Farzana knows that the additive identity property states
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!