Question

Triangle ABC is shown.

Given: ∆ABC

Prove: All three angles of ∆ABC add up to 180°.

The flow chart with missing reason proves the measures of the interior angles of ∆ABC total 180°.

Which reason can be used to fill in the numbered blank space?

Definition of Supplementary Angles

Substitution

Definition of Complementary Angles

Angle Addition Postulate

Answer 1

look at the tail boxes of two arrows

Answer 2

Tail boxes?

Answer 3

Okay, I'm looking at the boxes @ganeshie8

Answer 4

what do u notice

Answer 5

They both have m <EBD

Answer 6

they're just replacing \(m\angle EBD\) with \(180\) eh ?

Answer 7

so thats just a "Substitution" !

Answer 8

Oh! So all they did was substitute 180 for m<EBD?

Answer 9

yep !

Answer 10

Thank You! I have a couple more, I don't know if you're able to help me? @ganeshie8

Answer 11

sure post them il see if i can help :)

Answer 12

In ∆ABC, segment AB is congruent to segment BC .

Given: AB ≅ BC

Prove: The base angles of an isosceles triangle are congruent.

The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent.

Which statement can be used to fill in the numbered blank space?

∆DAB ≅ ∆DBC

∆ABD ≅ ∆ABC

∆ABC ≅ ∆CBD

∆ABD ≅ ∆CBD

@ganeshie8

Answer 13

you have any ideas

Answer 14

@ganeshie8 not completely. This is all new to me, I've just begun to learn it today.

Answer 15

I see, this is simple though, try to follow me :)

Answer 16

Okay

Answer 17

4th row has a blank,

Answer 18

previous rows that we have established these :-

\(BD \cong BD\)

\(\angle ABD \cong \angle DBC\)

\(AB \cong BC\)

Answer 19

Side
Angle
Side

Answer 20

that makes \(\triangle ABD \cong \triangle CBD\) by SAS postulate

Answer 21

Ah! Okay. I get it.

Answer 22

good :)