Chapter 4: Q11. (page 150)

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).
Given: $\bar{DE} ≅ \bar{FG}; \bar{GD} ≅ \bar{EF}$ ;
$∠ HDE and ∠ KFG are rt . ∠ s$
Prove: $\bar{DH} ≅ \bar{FK}$

Short Answer

Expert verified

$Δ GDE ≅ Δ EFG$	SSS postulate
$∠ DEG ≅ ∠ FGE$	Corr. Parts of $≅ Δ$ are $≅$ .
$Δ HDE ≅ Δ KFG$	ASA postulate
$\bar{DH} ≅ \bar{FK}$	Corr. Parts of $≅ Δ$ are $≅$ .

Step by step solution

Step 1. Description of step.

Consider $Δ G D E$ and $Δ E F G$ . From the given figure it can be observed that $\bar{D E} ≅ \bar{F G}, \bar{G D} ≅ \bar{E F}$ and $\bar{E G} ≅ \bar{E G}$ then by SSS postulate, $Δ G D E ≅ Δ E F G$ .

Step 2. Description of step.

As $Δ G D E ≅ Δ E F G$ then by corresponding parts of congruent triangles, $∠ D E G ≅ ∠ F G E$ .

Step 3. Description of step.

Consider $Δ H D E$ and $Δ K F G$ . From the given figure it can be observed that $\bar{D E} ≅ \bar{F G}$ , $∠ H D E ≅ ∠ K F G$ and $∠ D E H ≅ ∠ F G K$ then by ASA postulate, $Δ H D E ≅ Δ K F G$ .

Step 4. Description of step.

As $Δ H D E ≅ Δ K F G$ then by corresponding parts of congruent triangles, $\bar{D H} ≅ \bar{F K}$ .

Step 5. Key steps of a proof.

Make a list of key steps of a proof.

$Δ G D E ≅ Δ E F G$	SSS postulate
$∠ D E G ≅ ∠ F G E$	Corr. Parts of $≅ Δ$ are $≅$ .
$Δ H D E ≅ Δ K F G$	ASA postulate
$\bar{D H} ≅ \bar{F K}$	Corr. Parts of $≅ Δ$ are $≅$ .

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Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).
Given: $\bar{DE} ≅ \bar{FG}; \bar{GD} ≅ \bar{EF}$ ;
$∠ HDE and ∠ KFG are rt . ∠ s$
Prove: $\bar{DH} ≅ \bar{FK}$

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. Key steps of a proof.

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Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).Given: DE¯≅FG¯;GD¯≅EF¯;∠HDEand∠KFGarert.∠sProve: DH¯≅FK¯

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. Key steps of a proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Calculus

Applied Mathematics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).
Given: $\bar{DE} ≅ \bar{FG}; \bar{GD} ≅ \bar{EF}$ ;
$∠ HDE and ∠ KFG are rt . ∠ s$
Prove: $\bar{DH} ≅ \bar{FK}$