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2 years ago

ABCD is a parallelogram. E is the point where the diagonals AC and BD meet. Prove that triangle ABE is congruent to triangle CDE

Mathematics

2 answers:

iogann1982 [59]2 years ago

7 0

Answer:

Step-by-step explanation:

Given that ABCD is a parallelogram.

E is the point where the diagonals AC and BD meet.

Consider triangles ABE and CDE

Statement Reason

--------------------------------------------------------------------

1) AB =CD Opposite sides of a parallelogram

2) Angle ABE =

Angle EDC Alternate angles of two parallel lines

3) BE = DE Diagonals bisect each other in a parallelogram

Hence by SAS axiom the two triangles are congruent.

Darina [25.2K]2 years ago

5 0

ABCD is a parallelogram Given
AE=CE, BE=DE The diagonals of a parallelogram are bisect each other
∠AEB=∠CED Vertical angles are congruent
ΔABE is congruent to ΔCDE SAS theorem

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Answer:

Part A) The length of a straight line between the school and the Fire Station is $4.6\ miles$

Part B) The length of a straight line between the school and the hospital is $2.1\ miles$

Step-by-step explanation:

The complete question in the attached figure

Let

The positive x-coordinates ----> East

The positive y-coordinates ----> North

The negative x-coordinates ----> West

The negative y-coordinates ----> South

take the point A (0,0) as the Middle School (reference point)

Part A) we have

Town Hall is located 4.3 miles directly east of the Middle School

The coordinates of Town Hall are B(4.3,0)

The Fire Station is located 1.7 miles directly North of Town Hall

The coordinates of Fire Station are C(4.3,1.7)

What is the length of a straight line between the school and the Fire Station?

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(0,0) and C(4.3,1.7)

substitute

$d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}$

$d=\sqrt{(1.7)^{2}+(4.3)^{2}}$

$d=4.6\ miles$

Part B) we have that

The hospital is 3.1 miles west of the fire station

The coordinates of the hospital are D(4.3-3.1,1.7)

D(1.2,1.7)

What is the length of a straight line between the school and the hospital?

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(0,0) and D(1.2,1.7)

substitute

$d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}$

$d=\sqrt{(1.7)^{2}+(1.2)^{2}}$

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2 years ago

What is the range of the function f(x) = 3x2 + 6x – 8?

yawa3891 [41]

F(x) is a quadratic equation with the x-side squared and a is positive which means that the graph of the function is a parabola facing up. The range of f(x) is given by {y|y ≥ k}, where k is the y-coordinate of the vertex.
$f(x)=3 x^{2} +6x-8$ , written in vertex form is
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Answer:

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