If m< 1=53 degrees, what is m< 3. david states that def is an isosceles triangle. is he correct. explain

David states that DEF is an isosceles triangle.

David's statement is not correct.

Part 1

∠1 and angle ∠2 are complementary angles. They add to 90°.

So, ∠1 + ∠2 = 90°

53° +∠2  = 90°

∠2 = 90° - 53°

∠2 = 37°

Subtract this result from 180° to get the value of ∠3. This is because ∠2 and ∠3 are supplementary angles. They are a linear pair (the angles form a straight line).

∠3 = 180° - ∠2

∠3 = 180° - 37°

∠3 = 143°

note: you can add the remote interior angles at D and E to get 90+53 = 143 and you get the same answer. This is using the exterior angle theorem.

Part 2

In order for the triangle to be isosceles, the two acute angles (∠1, ∠2) must be congruent. Call them x for now. They must also add to 90°, so x+x = 90° leads to 2x = 90° and solves to x = 45°. Both angle 1 and angle 2 must be 45 degrees. However, angle 1 is 53 degrees and angle 2 is 37 degrees. So that is why David's statement is not correct.

Therefore, David's statement is not correct.

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Angle 3 is 143 degrees

He is not correct. The triangle is not isosceles.

Part 1

Angle 1 and angle 2 are complementary angles. They add to 90 degrees. So

(angle1) + (angle2) = 90

53 + (angle2) = 90

angle2 = 90 - 53

angle2 = 37 degrees

Subtract this result from 180 to get the value of angle 3. This is because angle 2 and angle 3 are supplementary angles. They are a linear pair (aka the angles form a straight line)

angle3 = 180 - (angle2)

angle3 = 180 - 37

angle3 = 143 degrees

note: you can add the remote interior angles at D and E to get 90+53 = 143 and you get the same answer. This is using the exterior angle theorem.

Part 2

In order for the triangle to be isosceles, the two acute angles (angle 1, angle 2) must be congruent. Call them x for now. They must also add to 90, so x+x = 90 leads to 2x = 90 and solves to x = 45. Both angle 1 and angle 2 must be 45 degrees. However, angle 1 is 53 degrees and angle 2 is 37 degrees. So that is why David's statement is not correct.

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²