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Chapter 4: Q8. (page 131)

Write proofs in two鈥揷olumn form.

Given: AD炉鈮�ME炉;AD炉鈭�ME炉

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

Short Answer

Expert verified

Statement

Reason

1.AD炉鈮�ME炉

Given

2.鈭�DAM鈮�鈭�EMB

Corresponding angles

3.AM炉鈮�MB炉

Definition of midpoint

4.螖DAM鈮�螖EMB

SAS congruency criteria

5.鈭�DMA鈮�鈭�EBM

corresponding parts of congruent triangle are congruent

6.MD炉鈭�BE炉

When transversal line intersect two lines such that corresponding angles are congruent then lines are parallel.

Step by step solution

01

Step 1. Observe from figure.

Line segmentAB炉 is transversal to parallel linesAD炉鈭�ME炉

02

Step 2. Show that ∠DAM≅∠EMB.

Since鈭�DAMand鈭�EMB forms a pair of corresponding angles

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

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 and using given statement螖DAM鈮�螖EMB by SAS (Side-Angle-Side) congruency criteria

05

Step 5. Show that ∠DMA≅∠EBM.

Since, corresponding parts of congruent triangle are congruent

Thus,鈭�DMA鈮�鈭�EBM

06

Step 6. Show that MD¯∥BE¯.

Since鈭�DMA鈭�鈭�EBM forms a pair of corresponding angles

When transversal line intersect two lines such that corresponding angles are congruent then lines are parallel. Thus, MD炉鈭�BE炉

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Most popular questions from this chapter

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

螖ABO鈮�螖___

Plot the given points on graph paper. Draw 螖FAT. Locate point Cso that role="math" localid="1638337170606" 螖FAT鈮�螖CAT.

role="math" localid="1638337180452" F7,5role="math" localid="1638337224388" A-2,2role="math" localid="1638337234009" T5,2

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?

OR炉is a common side of two congruent quadrilaterals.

Complete: quad.NERO鈮�quad?炉.
See all solutions

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