a. ABAE = ABDE b. ZDBC = 2DBE + ZBED c. ZABE + ZEBD = 2BAE + ZBCD %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Review Problems
1. Name three exterior angles of AADB in the fol-
lowing figure.
B
a. ABAE = ABDE
b. ZDBC = ZDBE + ZBED
c. ZABE + ZEBD = ZBAE + ZBCD
4. Given that points A, B, D, and E in the following
figure are collinear and
ZCBA = ZCDE.
2. Find the value of x.
BC = DC, prove
3x+30
2r-15°
x+ 69°
C
3. In the following figure with right angles as marked,
BE bisects LAED. Determine whether each state-
ment is always true or may be false. If true, explain
why.
A
B
D
Transcribed Image Text:Review Problems 1. Name three exterior angles of AADB in the fol- lowing figure. B a. ABAE = ABDE b. ZDBC = ZDBE + ZBED c. ZABE + ZEBD = ZBAE + ZBCD 4. Given that points A, B, D, and E in the following figure are collinear and ZCBA = ZCDE. 2. Find the value of x. BC = DC, prove 3x+30 2r-15° x+ 69° C 3. In the following figure with right angles as marked, BE bisects LAED. Determine whether each state- ment is always true or may be false. If true, explain why. A B D
3. Prove or disprove the statements in parts (a) and
(b) of #3 on p. 290
Transcribed Image Text:3. Prove or disprove the statements in parts (a) and (b) of #3 on p. 290
Expert Solution
Step 1

RHS congreuence rule:- if in two right triangles the hyotenuse and one side of one triangle are equal to thehypotenuse and one side of the other triangle, then the two triangle are congruent.a In BAE , BAE =90°In BDE , BDE =90°Given line BE bisects  AED AEB=BEDSo, the sides opposite to angle AEB and BED are also equal in BAE and BDEAB=BDthus , by RHS congreuence rule, in right angle triangle BAE and BDEhyotenuse BE=BE also one side AB=BDBAE  BDE

Step 2

b To check DBC =DBE+BEDsolution:- we know sum of all angle of a  is 180°In BEDBED +BDE+DBE=180°DBE+BED=180°-90°       BDE=90°                               = 90°So, we have to check DBC =90° or not let if posible DBC =90°also, we have BDE=90°If BD line acts as a transversal line then BC and DC should be parallel line because DBC=BDC     [alternate interior angle]But BC and DC are not parallel lines as we see in the diagram DBC90°so, DBC DBE+BEDGiven statement is False

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