Math / Geometry

QuestionHere is parallelogram $A B C D$ :
Prove segment $A M$ is congruent to segment $C M$ . Type your response in the space below.
B $I$
U Type here

Studdy Solution

STEP 1

1. $ABCD$ is a parallelogram.
2. Diagonals $AC$ and $BD$ intersect at point $M$ .
3. We need to prove that segment $AM$ is congruent to segment $CM$ .

STEP 2

1. Recall properties of a parallelogram.
2. Use the property of diagonals in a parallelogram.
3. Conclude the proof.

STEP 3

Recall properties of a parallelogram:
- Opposite sides are parallel and equal in length. - Diagonals bisect each other.

STEP 4

Use the property of diagonals in a parallelogram:
Since $ABCD$ is a parallelogram, its diagonals $AC$ and $BD$ bisect each other at point $M$ . This means:
$AM = MC$ $BM = MD$

STEP 5

Conclude the proof:
Since $AM = MC$ , segment $AM$ is congruent to segment $CM$ .
The proof is complete, and we have shown that segment $AM$ is congruent to segment $CM$ .

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QuestionHere is parallelogram $A B C D$ :
Prove segment $A M$ is congruent to segment $C M$ . Type your response in the space below.
B $I$
U Type here

Studdy Solution

STEP 1

1. $ABCD$ is a parallelogram.
2. Diagonals $AC$ and $BD$ intersect at point $M$ .
3. We need to prove that segment $AM$ is congruent to segment $CM$ .

STEP 2

1. Recall properties of a parallelogram.
2. Use the property of diagonals in a parallelogram.
3. Conclude the proof.

STEP 3

Recall properties of a parallelogram:
- Opposite sides are parallel and equal in length. - Diagonals bisect each other.

STEP 4

Use the property of diagonals in a parallelogram:
Since $ABCD$ is a parallelogram, its diagonals $AC$ and $BD$ bisect each other at point $M$ . This means:
$AM = MC$ $BM = MD$

STEP 5

Conclude the proof:
Since $AM = MC$ , segment $AM$ is congruent to segment $CM$ .
The proof is complete, and we have shown that segment $AM$ is congruent to segment $CM$ .

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QuestionHere is parallelogram ABCDA B C DABCD :Prove segment AMA MAM is congruent to segment CMC MCM. Type your response in the space below.B IIIU Type here

Studdy Solution

STEP 1

1. ABCDABCDABCD is a parallelogram.2. Diagonals ACACAC and BDBDBD intersect at point MMM.3. We need to prove that segment AMAMAM is congruent to segment CMCMCM.

STEP 2

1. Recall properties of a parallelogram.2. Use the property of diagonals in a parallelogram.3. Conclude the proof.

STEP 3

Recall properties of a parallelogram:- Opposite sides are parallel and equal in length. - Diagonals bisect each other.

STEP 4

Use the property of diagonals in a parallelogram:Since ABCDABCDABCD is a parallelogram, its diagonals ACACAC and BDBDBD bisect each other at point MMM. This means:AM=MC AM = MC AM=MC BM=MD BM = MD BM=MD

STEP 5

Conclude the proof:Since AM=MCAM = MCAM=MC, segment AMAMAM is congruent to segment CMCMCM. The proof is complete, and we have shown that segment AMAMAM is congruent to segment CMCMCM.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHere is parallelogram $A B C D$ :
Prove segment $A M$ is congruent to segment $C M$ . Type your response in the space below.
B $I$
U Type here

1. $ABCD$ is a parallelogram.
2. Diagonals $AC$ and $BD$ intersect at point $M$ .
3. We need to prove that segment $AM$ is congruent to segment $CM$ .

1. Recall properties of a parallelogram.
2. Use the property of diagonals in a parallelogram.
3. Conclude the proof.

Recall properties of a parallelogram:
- Opposite sides are parallel and equal in length. - Diagonals bisect each other.

Use the property of diagonals in a parallelogram:
Since $ABCD$ is a parallelogram, its diagonals $AC$ and $BD$ bisect each other at point $M$ . This means:
$AM = MC$ $BM = MD$

Conclude the proof:
Since $AM = MC$ , segment $AM$ is congruent to segment $CM$ .
The proof is complete, and we have shown that segment $AM$ is congruent to segment $CM$ .