Chapter 4: Q5. (page 129)

Describe your plan for proving the following.
Given: $\bar{C D} ⊥ \bar{A B}; D$ is midpoint of $\bar{A B}$ Prove: $\bar{C A} ≅ \bar{C B}$

Short Answer

Expert verified

$\bar{C D} ≅ \bar{C D}$ (reflexive property)

$\bar{A D} ≅ \bar{B D}$ (D is midpoint)

$Δ A D C ≅ Δ B D C$ (SAS congruence criteria)

$\bar{C A} ≅ \bar{C B}$ (corresponding parts of congruent triangles)

Step by step solution

Step 1. Show CD¯≅CD¯.

According to reflexive property of congruence, a line segment is congruent to itself.

Step 2. Show AD¯≅BD¯.

Using given statement $\bar{A D} ≅ \bar{B D}$

Step 3. Show ΔADC≅ΔBDC.

According to SAS congruence criteria, two triangles are said to be congruent if two sides and including angles of one triangle are congruent to the two sides and including angles of another triangle

So, from step 1, step 2 and $m ∠ A D C = m ∠ B D C = 90 °$

$Δ A D C ≅ Δ B D C$

Step 4. Show CA¯≅CB¯.

As corresponding parts of congruent triangles are equal

So, $\bar{C A} ≅ \bar{C B}$

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Describe your plan for proving the following.
Given: $\bar{C D} ⊥ \bar{A B}; D$ is midpoint of $\bar{A B}$ Prove: $\bar{C A} ≅ \bar{C B}$

Short Answer

Step by step solution

Step 1. Show CD¯≅CD¯.

Step 2. Show AD¯≅BD¯.

Step 3. Show ΔADC≅ΔBDC.

Step 4. Show CA¯≅CB¯.

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Describe your plan for proving the following.Given: CD¯⊥AB¯;Dis midpoint of AB¯Prove: CA¯≅CB¯

Short Answer

Step by step solution

Step 1. Show CD¯≅CD¯.

Step 2. Show AD¯≅BD¯.

Step 3. Show ΔADC≅ΔBDC.

Step 4. Show CA¯≅CB¯.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Probability and Statistics

Applied Mathematics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Describe your plan for proving the following.
Given: $\bar{C D} ⊥ \bar{A B}; D$ is midpoint of $\bar{A B}$ Prove: $\bar{C A} ≅ \bar{C B}$