Mathematics High School

I WILL AWARD BRAINLIEST!! PLEASE HELP!!


Given: AC = AB, CD = DE

m∠ABC = 70°, m∠ ECB = 35°


Prove: DE ║BC



m∠ACB = m∠______, By reason ( Base angles theorem, Exterior Angle theorem, Supplementary angles, Vertical Angles theorem ) - choose one

Answers

Answer 1

Answer:

a)[tex]\angle ACB = \angle ABC[/tex] By Base angle theorem

b)DE||BC since[tex]\angle DEC=\angle ECB[/tex] and they are alternate interior angles

Step-by-step explanation:

Given: AC = AB, CD = DE

∠ABC = 70°, m∠ ECB = 35°

Refer the attached figure

AB = AC

So, By Base angle theorem : if the sides of a triangle are congruent then the angles opposite these sides are congruent.

So, [tex]\angle ACB = \angle ABC[/tex]

So,[tex]\angle ACB = \angle ABC =70^{\circ[/tex]      ----1

CD = DE

So, by Base theorem

[tex]\angle DCE = \angle DEC[/tex]

Let [tex]\angle DCE[/tex]  be x

So,[tex]\angle DCE = \angle DEC[/tex]

[tex]\angle ACB= \angle DCE+\angle ECB = x+35[/tex]

Using 1

70 = x+35

35=x

[tex]\angle DCE = \angle DEC =35^{\circ}[/tex]

Now[tex]\angle DEC=\angle ECB=35^{\circ}[/tex]

So, DE||BC since[tex]\angle DEC=\angle ECB[/tex] and they are alternate interior angles

I WILL AWARD BRAINLIEST!! PLEASE HELP!!Given: AC = AB, CD = DEmABC = 70, M ECB = 35 Prove: DE BC MACB

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