Chapter 4: Q30. (page 139)

Given: $Δ ABC$ in plane M; D not in plane M;
$∠ ACB ≅ ∠ ABC; ∠ DCB ≅ ∠ DBC$
Name a pair of congruent triangles. Prove that your answer is correct.

Short Answer

Expert verified

A pair of congruent triangles is $Δ ACD$ and $Δ ABD$ .

Step by step solution

– Description of step.

If two angles of triangle are congruent then the sides opposite to those angles are congruent.

It is given that, $∠ A C B ≅ ∠ A B C$ . Therefore, by converse isosceles triangle theorem, $\bar{A B} ≅ \bar{A C}$ .

– Description of step.

If two angles of triangle are congruent then the sides opposite to those angles are congruent.

It is given that, $∠ D C B ≅ ∠ D B C$ . Therefore, by converse isosceles triangle theorem, $\bar{D B} ≅ \bar{D C}$ .

– Reflexive property.

Reflexive property states that, $\bar{P Q} ≅ \bar{P Q}$ . Therefore, in this case by reflexive property, $\bar{A D} ≅ \bar{A D}$ .

– SSS postulate.

If three sides of one triangle are congruent to three sides of other triangle then the triangles are congruent.

Here, $\bar{A B} ≅ \bar{A C}$ , $\bar{D B} ≅ \bar{D C}$ and $\bar{A D} ≅ \bar{A D}$ then by $S S S$ postulate $Δ A C D ≅ Δ A B D$ .

Therefore, a pair of congruent triangles is $Δ A C D$ and $Δ A B D$ .

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Given: $Δ ABC$ in plane M; D not in plane M;
$∠ ACB ≅ ∠ ABC; ∠ DCB ≅ ∠ DBC$
Name a pair of congruent triangles. Prove that your answer is correct.

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Reflexive property.

– SSS postulate.

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Given:ΔABC in plane M; D not in plane M;∠ACB≅∠ABC;∠DCB≅∠DBCName a pair of congruent triangles. Prove that your answer is correct.

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Reflexive property.

– SSS postulate.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Given: $Δ ABC$ in plane M; D not in plane M;
$∠ ACB ≅ ∠ ABC; ∠ DCB ≅ ∠ DBC$
Name a pair of congruent triangles. Prove that your answer is correct.