Question

In Triangle ABC shown below, side AB is 8 and side AC is 4.

Which statement is needed to prove that segment DE is half the length of segment BC?

Segment AD is 4 and segment AE is 8.

Segment AD is 2 and segment AE is 4.

Segment AD is 4 and segment AE is 2.

Segment AD is 2 and segment AE is 2.

Answer 1

@ganeshie8

Answer 2

@ganeshie8

Answer 3

I think it's between the last two options because segment AE can't be anymore than 2, and segment AD looks to be about 4, so option 3?

Answer 4

good guess :)

Answer 5

And E is the midpoint between AC, and AC is 4 so that makes AE 2

Answer 6

use this :

AD = AB/2
AE = AC/2

Answer 7

AB is 8, and D is the midpoint between AB, so AD must be 4

Answer 8

thats it ! you figured teh answer urself :))

Answer 9

I'm definitely trying, but you are a big help! Okay, I have this one:

Gordon is writing a proof of the theorem stated below.

Theorem: The sum of interior angles of a triangle is 180°.

He first drew the figure shown below.

Which theorem will he most likely use in the proof?

a) Supplements of congruent angles are congruent.

b) A linear pair of angles is supplementary.

c) If two angles of a triangle are congruent, the sides opposite these are congruent.

d) If two sides of a triangle are congruent, the angles opposite these sides are congruent.

Answer 10

@ganeshie8 I think the answer is b, am I right?

Answer 11

b is right !

Answer 12

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 28°.

The flow chart with missing statements and reasons proves that the measure of angle ECB is 62°.

Which statement and reason can be used to fill in the numbered blank spaces?

1. Base angle theorem
2. Corresponding angle are congruent
3. Measure of angle AED is 28°.

1. Alternate interior angles are congruent
2. Base angle theorem
3. Measure of angle AED is 62°.

1. Corresponding angles are congruent
2. Triangle Sum Theorem
3. Measure of angle AED is 28°.

1. Corresponding angles are congruent
2. Triangle Sum Theorem
3. Measure of angle AED is 62°.

Answer 13

Between choice 2 and choice 4

Answer 14

Because AED and ECB are congruent, and ECB measures 62 degrees

Answer 15

I think its choice 4, because I don't think alternate interior angles is the answer

Answer 16

perfect ! thats the correct one !!

Answer 17

Thank you! Okay so this one:

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG.

Which conclusion can be made based on the given conditions?

Segment GF is congruent to segment EG. ---> this isn't true

Segment GF is half the length of segment EB. ---> this isn't true

Segment GD is congruent to segment EG. --> it's this one

Segment GD is half the length of segment HC. ----> Or this one

Answer 18

@ganeshie8