Basic Engineering Mathematics, Fifth Edition

Angles and triangles 175

(a) (b)

568299

148419

a

b

688

1318

c

d e

g

f

Figure 20.32

9. Find the unknown angles a to k in
   Figure 20.33.

998

1258

228 b d

a c

k

e g h

f

j i

Figure 20.33

10. TriangleABChas a right angle at Band
    ∠BACis 34◦.BCis produced toD.Ifthe
    bisectors of∠ABCand∠ACDmeet atE,
    determine∠BEC.


11. Ifin Figure20.34triangleBCDisequilateral,
    find the interior angles of triangleABE.

978

A

B

C

D

E

Figure 20.34

20.4 Congruent triangles

Two triangles are said to becongruentif they are equal
in all respects; i.e., three angles and three sides in one
triangle are equal to three angles and three sides in the
other triangle. Two triangles are congruent if

(a) the three sides of one are equal to the three sides

of the other (SSS),

(b) two sides of one are equal to two sides of the other

and the angles included by these sides are equal

(SAS),

(c) two angles of the one are equal to two angles of

the other and any side of the first is equal to the

corresponding side of the other (ASA), or

(d) their hypotenuses are equal and one other side of

one is equal to the corresponding side of the other

(RHS).

Problem 24. State which of the pairs of triangles

shown in Figure 20.35 are congruent and name their

sequence

(c)

M

N

P

O

Q

R

(d)

S

T

V U

W X

(e)

F

D E

B

A

C

(a) (b)

A

B

C

E D

F K

L

H J

G

I

Figure 20.35

(a) CongruentABC, FDE(angle, side, angle; i.e.,

ASA).

(b) CongruentGIH,JLK(side, angle, side; i.e., SAS).

(c) CongruentMNO,RQP(right angle, hypotenuse,

side; i.e., RHS).

(d) Not necessarily congruent. It is not indicated that

any side coincides.

(e) Congruent ABC, FED (side, side, side; i.e.,

SSS).