Chapter 4: Q15. (page 151)

Given: $\bar{AM} ≅ \bar{MB}; \bar{AD} ≅ \bar{BC}$
$∠ MDC ≅ ∠ MCD$
Prove: $\bar{AC} ≃ \bar{BD}$

Short Answer

Expert verified

$Δ ADM ≅ Δ BCM$ by SSS postulate then by corresponding parts of congruent triangles $∠ ADC ≅ ∠ BCD$ . $Δ ADC ≅ Δ BCD$ by SAS postulate then corresponding parts of congruent triangles, $\bar{AC} ≅ \bar{BD}$ .

Step by step solution

Step 1. Description of step.

Consider $Δ A D M$ and $Δ B C M$ . From the given figure it can be observed that $\bar{A D} ≅ \bar{B C}$ , $\bar{D M} ≅ \bar{C M}$ and $\bar{A M} ≅ \bar{M B}$ then by SSS postulate, $Δ A D M ≅ Δ B C M$ .

Step 2. Description of step.

As $Δ A D M ≅ Δ B C M$ then by corresponding parts of congruent triangles $∠ A D M ≅ ∠ B C M$ and $∠ M D C ≅ ∠ M C D$ which implies that $∠ A D C ≅ ∠ B C D$ .

Step 3. Description of step.

Consider $Δ A D C$ and $Δ B C D$ . From the given figure it can be observed that $\bar{A D} ≅ \bar{B C}$ , $∠ A D C ≅ ∠ B C D$ and $\bar{C D} ≅ \bar{C D}$ then by SAS postulate, $Δ A D C ≅ Δ B C D$ .

Step 4. Description of step.

As $Δ A D C ≅ Δ B C D$ then by corresponding parts of congruent triangles, $\bar{A C} ≅ \bar{B D}$ .

Step 5. Write a paragraph proof.

$Δ A D M ≅ Δ B C M$ by SSS postulate then by corresponding parts of congruent triangles $∠ A D C ≅ ∠ B C D$ . $Δ A D C ≅ Δ B C D$ by SAS postulate then corresponding parts of congruent triangles, $\bar{A C} ≅ \bar{B D}$ .

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Given: $\bar{AM} ≅ \bar{MB}; \bar{AD} ≅ \bar{BC}$
$∠ MDC ≅ ∠ MCD$
Prove: $\bar{AC} ≃ \bar{BD}$

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write a paragraph proof.

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Given: AM¯≅MB¯;AD¯≅BC¯∠MDC≅∠MCDProve: AC¯≃BD¯

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write a paragraph proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Statistics

Applied Mathematics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Given: $\bar{AM} ≅ \bar{MB}; \bar{AD} ≅ \bar{BC}$
$∠ MDC ≅ ∠ MCD$
Prove: $\bar{AC} ≃ \bar{BD}$