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Chapter 4: Q7. (page 131)

Write proofs in two鈥揷olumn form.

Given:AD炉鈭�ME炉;MD炉鈭�BE炉

Mis the midpoint of AB炉. Prove: MD炉鈮�BE炉

Short Answer

Expert verified

Statement

Reason

1.鈭�DAM鈮�鈭�EMB

Corresponding angles

2.AM炉鈮�MB炉

Definition of midpoint

3.鈭�DMA鈮�鈭�EBM

Corresponding angles

4.width="113" height="20" role="math">螖DAM鈮�螖EMB

ASA congruency criteria

5.width="67" height="23" role="math">MD炉鈮�BE炉

corresponding parts of congruent triangle are congruent

Step by step solution

01

Step 1. Observe from figure.

Line segmentAB炉 is transversal to parallel linesAD炉鈭�ME炉;MD炉鈭�BE炉

02

Step 2. Show that ∠DAM≅∠EMB; ∠DMA≅∠EBM.

Since鈭�DAM鈭�鈭�EMB and鈭�DMA鈭�鈭�EBM form pairs of corresponding angles

When transversal line intersect two parallel lines then corresponding angles are congruent. Thus,鈭�DAM鈮�鈭�EMB;鈭�DMA鈮�鈭�EBM

03

Step 3. Show that AM¯≅MB¯.

By definition of midpoint, midpoint divides line segment in two congruent line segments

AM炉鈮�MB炉

04

Step 4. Show that ΔDAM≅ΔEMB.

From step 2 and 3螖DAM鈮�螖EMB by ASA (Angle-Side-Angle) congruency criteria

05

Step 5. Show that MD¯≅BE¯.

Since, corresponding parts of congruent triangle are congruent

Thus,MD炉鈮�BE炉

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Most popular questions from this chapter

Suppose you know that DB炉鈯�DC炉.Explain how you can deduce that DB炉鈯�BA炉.

Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

If a line perpendicular to AB炉passes through the midpoint of AB炉, and segments are drawn from any other point on that line to and , then two congruent triangles are formed.

Suppose that 螖BIG鈮�螖CAT, then complete the following statement.

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In the following figure, the two-triangle shown are congruent. Then explain the following statement.

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