Regardless of the side length, if the area of a square is quadrupled, the side lengths get doubled, as shown in the diagram. If all of the side lengths are doubled, that means the perimeter is also doubled.

8 0

3 years ago

In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC

Makovka662 [10]

Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

3 0

3 years ago

Dario bakes a lasagna containing 2/3 pound of parmesan cheese, 5/4 pounds of ricotta cheese, and 4/3 pounds of mozzarella cheese

kap26 [50]

First, we have to figure out how much cheese we have total. Do this by adding up all of the various cheeses.

$\frac{2}{3} + \frac{4}{3} + \frac{5}{4} \\ \frac{6}{3} + 1 + \frac{1}{4} \\ 3 \frac{1}{4}$
Now to split the cheeses into sections of 1/4 pound each, we have to divide by 1/4, which is the same as multipling by 4

$3 \frac{1}{4} \times 4 = 12 + 1 = 13$

13 slices total

5 0

3 years ago

Could u help me ? I really can’t figure this out it’s driving me crazy

Irina18 [472]

Answer:

The answer is 1

One

Uno

Aight nvm

By adding 5 to both side we will just get x2= -4+5

-4+5=1

7 0

3 years ago