Prove that if a quadrilateral has four equal sides and one right angle, then the quadrilateral is a square

1 answer:

3 0

So lets ABCD are the sides of the square and AB=CD, AC=BD and the Angle ABC = 90 so therefore by making a diagonal we can use the SAS or SSS congruency for two triangles, so we can prove two triangles are equal and that is why the shape is square.

You might be interested in

Find the slope of the line

attashe74 [19]

slope = $\frac{3}{2}$

To calculate the slope m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁) = (- 2, 0 ) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = $\frac{3-0}{0+2}$ = $\frac{3}{2}$

4 0

3 years ago

Read 2 more answers

Juan and Raj cut up a banana to put on cereal. Juan puts 17 of the banana on his bowl of cereal, and Raj puts 25 of the banana

rusak2 [61]

<h3><u>Question:</u></h3>

Juan and raj cut up a banana to put on cereal. juan puts 1/7 of the banana on his bowl of cereal, and raj puts 2/5 of the banana on his bowl of cereal.

what fraction of the banana did juan and raj put on their cereal altogether?

a. 2/35 banana

b. 3/12 banana

c. 3/7 banana

d. 19/35 banana

<h3><u>Answer:</u></h3>

Juan and Raj altogether put 19/35 banana

<h3><u>Solution</u>:</h3>

Given that, Juan and Raj cut up a banana to put on cereal

$fraction\ of\ banana\ put\ by\ Juan = \frac{1}{7}\\\\fraction\ of\ banana\ put\ by\ Raj = \frac{2}{5}$

We have to find the fraction of banana put by Juan and Raj altogether

This means, we have to add both the fractions

$fraction\ of\ banana\ put\ altogether = fraction\ of\ banana\ put\ by\ Juan + fraction\ of\ banana\ put\ by\ Raj$

$fraction\ of\ banana\ put\ altogether = \frac{1}{7} + \frac{2}{5}\\\\\text{Cross multiply to simplify }\\\\fraction\ of\ banana\ put\ altogether = \frac{1 \times 5 + 2 \times 7}{7 \times 5}\\\\fraction\ of\ banana\ put\ altogether = \frac{5+14}{35}\\\\fraction\ of\ banana\ put\ altogether = \frac{19}{35}$