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2 years ago

Given: Quadrilateral PQRS is a rectangle. Prove: PR = QS

Mathematics

1 answer:

lord [1]2 years ago

6 0

Answer:

Given: Quadrilateral P QR S is a rectangle.

To prove :PR= Q S

Construction : Join PR and Q S.

Proof: In Rectangle PQRS, and

→ taking two triangles PSR and Δ QRS

1. PS = Q R

2. ∠ PS R = ∠ Q RS [Each being 90°]

3. S R is common.

→ ΔP SR ≅ Δ Q RS → [Side-Angle-Side Congruency]

∴ PR =Q S [ corresponding part of congruent triangles ]

Hence proved.

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If ∠C and ∠D are vertical angles and m ∠ C = x + 5 and m ∠ D = –2x + 80, what is m ∠ C?

amm1812

Answer:

m∠C=30°

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always equal

m∠C=m∠D

substitute the given values

$(x+5)\°=(-2x+80)\°$

Solve for x

$x+2x=80-5\\3x=75\\x=25$

Find the measure of angle C

m∠C=(x+5)°

substitute the value of x

m∠C=(25+5)=30°

3 0

2 years ago

Adonis created a rectangular play area for his dog in his backyard. The length of the long side was 10ft and the length of the s

Drupady [299]

Answer:

The perimeter of the dog's play area is 30 ft

Step-by-step explanation:

Rectangle:

The opposite sides are congruent.
The opposite angles are congruent.
The sum of all four angles of a rectangle is 360°.
The sum of two adjacent angles of a rectangle is 180°.
The diagonals bisect each other.
The perimeter of a rectangle is = 2(Length+width)
The area of a rectangle is = Length × width

Given that,

The length of the long side of the dog's play area was = 10 ft.

So, Length of dog's play area is = 10 ft.

The length of the short side of the dog's play area was = 5 ft.

So, width of dog's play area is = 5 ft.

It is a rectangular plot.

So, the perimeter of the dog's play area is =2(Length+width)

=2(10+5) ft

=2(15) ft

=30 ft

5 0

3 years ago

Is this true? And also how does the equation from y-3=3(x-4) become a positive y+3=3x-12?

EastWind [94]

Step-by-step explanation:

the right equation is :

y-y1=m(x-x1)

y+3=3(x+4)

y+3= 3x+12

y=3x+12-3

y=3x+9

7 0

2 years ago

A family of two adults and three children goes to a play admission costs eight dollars per adult and $5 per child. What expressi

Sidana [21]

D = adult
c = child
t = total admission cost

t = 8d + 5c

t = 8(2) + 5(3) = $31

5 0

3 years ago

Plz don't answer unless you will do all ty

liberstina [14]

The answer would be D

7 0

2 years ago