Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 36°.

Triangle ABC with segment DE. Angle ADE measures 36 degrees.

The proof, with a missing reason, proves that the measure of angle ECB is 54°.

Statement Reason
m∠ADE = 36° Given
m∠DAE = 90° Definition of a right angle
m∠AED = 54° Triangle Sum Theorem
segment DE joins the midpoints of segment AB and segment AC Given
segment DE is parallel to segment BC ?
∠ECB ≅ ∠AED Corresponding angles are congruent
m∠ECB = 54° Substitution property

Which theorem can be used to fill in the missing reason?

A. Concurrency of Medians Theorem

B. Isosceles Triangle Theorem

C. Midsegment of a Triangle Theorem

D. Triangle Inequality Theorem

step-by-step explanation:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

answer: the is put the 450

step-by-step explanation: