MATH SOLVE

2 months ago

Q:
# please help! geometry problem 3!

Accepted Solution

A:

Comment

|First of all, the triangles are equal by ASA the way the diagram has been marked.

B and E are both right angles.

Side BC = Side DE

<BCA =< EDA

So triangle BCA = triangle EDA

Now to the letters.

x = y - 1 Add 1 to both sides.

x + 1 = y (1)

3x - 2 = 2y + 1 Subtract 1 from both sides.

3x -2 - 1 = 2y

3x - 3 = 2y Divide by 2

3x/2 - 3/2 = 2y/2

1.5x - 1.5 = y (2)

Step One

Since (1) and (2) both have y isolated on their respective right sides, they can be equated.

1.5x - 1.5 = x + 1 Take an x from both sides.

0.5x - 1.5 = x - x + 1

0.5x - 1.5 = 1 Add 1.5 to both sides.

0.5x = 1 + 1.5

0.5x = 2.5 Divide 0.5 on both sides.

0.5x/0.5 = 2.5/0.5

x = 5

Now we need a y value.

x = y - 1

5 = y - 1 Add 1 to both sides.

5 + 1 = y - 1 + 1

6 = y

So the 2 sides and the 2 angles are equal when

x = 5

y = 6

C Answer <<<<<<

|First of all, the triangles are equal by ASA the way the diagram has been marked.

B and E are both right angles.

Side BC = Side DE

<BCA =< EDA

So triangle BCA = triangle EDA

Now to the letters.

x = y - 1 Add 1 to both sides.

x + 1 = y (1)

3x - 2 = 2y + 1 Subtract 1 from both sides.

3x -2 - 1 = 2y

3x - 3 = 2y Divide by 2

3x/2 - 3/2 = 2y/2

1.5x - 1.5 = y (2)

Step One

Since (1) and (2) both have y isolated on their respective right sides, they can be equated.

1.5x - 1.5 = x + 1 Take an x from both sides.

0.5x - 1.5 = x - x + 1

0.5x - 1.5 = 1 Add 1.5 to both sides.

0.5x = 1 + 1.5

0.5x = 2.5 Divide 0.5 on both sides.

0.5x/0.5 = 2.5/0.5

x = 5

Now we need a y value.

x = y - 1

5 = y - 1 Add 1 to both sides.

5 + 1 = y - 1 + 1

6 = y

So the 2 sides and the 2 angles are equal when

x = 5

y = 6

C Answer <<<<<<