Math / Geometry

Question0 W
Using the AAS Congruence Theorem, what other information proves $\triangle B I G \cong \triangle C O W$ ? (1 point) $\overline{B I} \cong \overline{C O}$ $\angle I \cong \angle O$ $\overline{B G} \cong \overline{C W}$ $\overline{G B} \cong \overline{W C}$

Studdy Solution

STEP 1

What is this asking? Figure out which piece of information, when combined with two angles, shows that $\triangle B I G$ is congruent to $\triangle C O W$ using the Angle-Angle-Side (AAS) Theorem. Watch out! Don't confuse the AAS Theorem with other congruence theorems like SAS or ASA.
We need two angles and a non-included side!

STEP 2

1. Understand the AAS Congruence Theorem
2. Identify the given angles
3. Determine the necessary side

STEP 3

The AAS Congruence Theorem tells us that two triangles are congruent if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
This means we need to find two pairs of equal angles and one pair of equal sides that is not between them!

STEP 4

We are told that $\angle I \cong \angle O$ .
This is one pair of angles.
We need another pair of angles to use the AAS Theorem.

STEP 5

Since we have $\angle I \cong \angle O$ , we need to find a side that is not between the two angles.
The side should be opposite one of the angles.

STEP 6

The side opposite $\angle I$ in $\triangle B I G$ is $\overline{B G}$ and the side opposite $\angle O$ in $\triangle C O W$ is $\overline{C W}$ .
Therefore, if $\overline{B G} \cong \overline{C W}$ , we can use the AAS Theorem to prove the triangles are congruent!

STEP 7

The missing piece of information is $\overline{B G} \cong \overline{C W}$ .

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Question0 W
Using the AAS Congruence Theorem, what other information proves $\triangle B I G \cong \triangle C O W$ ? (1 point) $\overline{B I} \cong \overline{C O}$ $\angle I \cong \angle O$ $\overline{B G} \cong \overline{C W}$ $\overline{G B} \cong \overline{W C}$

Studdy Solution

STEP 1

STEP 2

1. Understand the AAS Congruence Theorem
2. Identify the given angles
3. Determine the necessary side

STEP 3

The AAS Congruence Theorem tells us that two triangles are congruent if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
This means we need to find two pairs of equal angles and one pair of equal sides that is not between them!

STEP 4

We are told that $\angle I \cong \angle O$ .
This is one pair of angles.
We need another pair of angles to use the AAS Theorem.

STEP 5

Since we have $\angle I \cong \angle O$ , we need to find a side that is not between the two angles.
The side should be opposite one of the angles.

STEP 6

The side opposite $\angle I$ in $\triangle B I G$ is $\overline{B G}$ and the side opposite $\angle O$ in $\triangle C O W$ is $\overline{C W}$ .
Therefore, if $\overline{B G} \cong \overline{C W}$ , we can use the AAS Theorem to prove the triangles are congruent!

STEP 7

The missing piece of information is $\overline{B G} \cong \overline{C W}$ .

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Studdy Solution

STEP 1

STEP 2

1. Understand the AAS Congruence Theorem2. Identify the given angles3. Determine the necessary side

STEP 3

The AAS Congruence Theorem tells us that two triangles are congruent if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.This means we need to find two pairs of equal angles and one pair of equal sides that is not between them!

STEP 4

We are told that ∠I≅∠O\angle I \cong \angle O∠I≅∠O.This is one pair of angles.We need another pair of angles to use the AAS Theorem.

STEP 5

Since we have ∠I≅∠O\angle I \cong \angle O∠I≅∠O, we need to find a side that is not between the two angles.The side should be opposite one of the angles.

STEP 6

STEP 7

The missing piece of information is BG‾≅CW‾\overline{B G} \cong \overline{C W}BG≅CW.

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1. Understand the AAS Congruence Theorem
2. Identify the given angles
3. Determine the necessary side

The AAS Congruence Theorem tells us that two triangles are congruent if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
This means we need to find two pairs of equal angles and one pair of equal sides that is not between them!

We are told that $\angle I \cong \angle O$ .
This is one pair of angles.
We need another pair of angles to use the AAS Theorem.

Since we have $\angle I \cong \angle O$ , we need to find a side that is not between the two angles.
The side should be opposite one of the angles.

The missing piece of information is $\overline{B G} \cong \overline{C W}$ .