Math / Geometry

QuestionGiven: $\angle A$ and $\angle C$ are right angles; $\overline{A B} \cong \overline{C D}$ . Prove: $\triangle A B D \cong \triangle C D B$ Complete the proof. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Statements } & \multicolumn{1}{c|}{ Reasons } \\ \hline \begin{tabular}{l}
1. $\angle A$ and $\angle C$ are \\ right angles; $\overline{A B} \cong \overline{C D}$ . \end{tabular} & 1. \\ \hline \begin{tabular}{c}
2. $\triangle A B D$ and $\triangle C D B$ are \\ right triangles. \end{tabular} & 2. \\ \hline 3. $\overline{B D} \cong \overline{D B}$ & 3. \\ \hline 4. $\triangle A B D \cong \triangle C D B$ & 4. \\ \hline \end{tabular}
Drag the reasons to the correct order. (i) Instructions
LL Theorem
Definition of right triangle
Reflexive Property of Congruence
Given
Symmetric Property of Congruence HL Theorem

Studdy Solution

STEP 1

1. $\angle A$ and $\angle C$ are right angles.
2. $\overline{A B} \cong \overline{C D}$ .
3. We need to prove $\triangle A B D \cong \triangle C D B$ .

STEP 2

1. Identify the given information.
2. Determine the type of triangles.
3. Use properties of congruence.
4. Apply a congruence theorem to prove triangle congruence.

STEP 3

Identify the given information:
1. $\angle A$ and $\angle C$ are right angles; $\overline{A B} \cong \overline{C D}$ .
Reason: Given

STEP 4

Determine the type of triangles:
2. $\triangle A B D$ and $\triangle C D B$ are right triangles.
Reason: Definition of right triangle

STEP 5

Use properties of congruence:
3. $\overline{B D} \cong \overline{D B}$
Reason: Reflexive Property of Congruence

STEP 6

Apply a congruence theorem to prove triangle congruence:
4. $\triangle A B D \cong \triangle C D B$
Reason: HL Theorem
The proof is complete.

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Studdy Solution

STEP 1

1. $\angle A$ and $\angle C$ are right angles.
2. $\overline{A B} \cong \overline{C D}$ .
3. We need to prove $\triangle A B D \cong \triangle C D B$ .

STEP 2

1. Identify the given information.
2. Determine the type of triangles.
3. Use properties of congruence.
4. Apply a congruence theorem to prove triangle congruence.

STEP 3

Identify the given information:
1. $\angle A$ and $\angle C$ are right angles; $\overline{A B} \cong \overline{C D}$ .
Reason: Given

STEP 4

Determine the type of triangles:
2. $\triangle A B D$ and $\triangle C D B$ are right triangles.
Reason: Definition of right triangle

STEP 5

Use properties of congruence:
3. $\overline{B D} \cong \overline{D B}$
Reason: Reflexive Property of Congruence

STEP 6

Apply a congruence theorem to prove triangle congruence:
4. $\triangle A B D \cong \triangle C D B$
Reason: HL Theorem
The proof is complete.

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Studdy Solution

STEP 1

1. ∠A\angle A∠A and ∠C\angle C∠C are right angles.2. AB‾≅CD‾\overline{A B} \cong \overline{C D}AB≅CD.3. We need to prove △ABD≅△CDB\triangle A B D \cong \triangle C D B△ABD≅△CDB.

STEP 2

1. Identify the given information.2. Determine the type of triangles.3. Use properties of congruence.4. Apply a congruence theorem to prove triangle congruence.

STEP 3

Identify the given information:1. ∠A\angle A∠A and ∠C\angle C∠C are right angles; AB‾≅CD‾\overline{A B} \cong \overline{C D}AB≅CD.Reason: Given

STEP 4

Determine the type of triangles:2. △ABD\triangle A B D△ABD and △CDB\triangle C D B△CDB are right triangles.Reason: Definition of right triangle

STEP 5

Use properties of congruence:3. BD‾≅DB‾\overline{B D} \cong \overline{D B}BD≅DBReason: Reflexive Property of Congruence

STEP 6

Apply a congruence theorem to prove triangle congruence:4. △ABD≅△CDB\triangle A B D \cong \triangle C D B△ABD≅△CDBReason: HL Theorem The proof is complete.

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1. $\angle A$ and $\angle C$ are right angles.
2. $\overline{A B} \cong \overline{C D}$ .
3. We need to prove $\triangle A B D \cong \triangle C D B$ .

1. Identify the given information.
2. Determine the type of triangles.
3. Use properties of congruence.
4. Apply a congruence theorem to prove triangle congruence.

Identify the given information:
1. $\angle A$ and $\angle C$ are right angles; $\overline{A B} \cong \overline{C D}$ .
Reason: Given

Determine the type of triangles:
2. $\triangle A B D$ and $\triangle C D B$ are right triangles.
Reason: Definition of right triangle

Use properties of congruence:
3. $\overline{B D} \cong \overline{D B}$
Reason: Reflexive Property of Congruence

Apply a congruence theorem to prove triangle congruence:
4. $\triangle A B D \cong \triangle C D B$
Reason: HL Theorem
The proof is complete.