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PLEASE HELP I NEED TO PASS THIS TEST 

In ΔABC, and . D and E are the midpoints of and , respectively.

If the length of CA is 9 units, the length of DE is ____
units and mCAB is _____degrees

PLEASE HELP I NEED TO PASS THIS TEST In ΔABC and D and E are the midpoints of and respectively If the length of CA is 9 units the length of DE is units and mCAB class=

Respuesta :

mreijepatmat
This is an isosceles right triangle (AB = BC & ∠ B=90° - Given)
Then the angles at the base are equal and ∠ CAB = ∠ ACB = 45°

Theorem: Segment DE, joining the midpoints of 2 sides is:
                 1st) parallel to the 3rd side and
                 2nd) equal to half the measurement of the 3rd side
So if the 3rd side (hypotenuse) = 9 units, DE = 9/2 = 4.5 units

The length of DE is 4.5 units and ∠CAB= 45 degrees

What is Isosceles right triangle?

An isosceles right triangle has the characteristic of both the isosceles and the right triangles. It has two equal sides, two equal angles, and one right angle.

What is mid point theorem?

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Triangle ABC is and isosceles right triangle,

BC=BA

∠ABC=90 degrees

Therefore, ∠CAB=∠ACB = 45 degrees

Because sum of the angles in a triangle add up to 180 degrees

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Therefore,

DE= Half of CA

CA=9 units

DE= 4.5 units

Hence, the length of DE is 4.5 units and ∠CAB= 45 degrees

Learn more about Isosceles right triangle and mid point theorem here

https://brainly.com/question/12918136

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