Скачать или смотреть #Ex

@soeasymaths2791 Congruent Triangles, Rules of Congruent Triangles
chapter 7/class 9 th/Ex7.1/mathematics
EXERCISE 7.1

1. In quadrilateral ACBD, AC = AD and AB bisects A (see Fig. 7.16). Show that Delta ABC cong Delta*ABD What can you say about BC and BD
2. ABCD is a quadrilateral in which AD = BC and angle DAB = angle CBA (see Fig. 7.17). Prove that

(1) Delta ABD cong Delta*BAC

(ii) BD = AC

(iii) angle ABD = angle BAC.

3. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

Fig. 7.15

4. I and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that Delta ABC cong Delta*CDA

D

C

5. Line/ is the bisector of an angle ∠ A and B is any point on /. BP and BQ are perpendiculars from B to the arms of angle A (see Fig. 7.20). Show that:

(1) Delta APB cong Delta*AQB

(ii) BP = BQ or B is equidistant from the arms of angle A

In

Fig. 7.21, AC = AE AB = AD and angle BAD = angle EAC Show that B overline C = DE

∠C= 2

90

M

Proofs In ABC AB = AC(G) 1=L2=( Lola(0 = s / u) Im triangle ACO AB = AC = AD AC = 0

B

D

C

. 7. segment and P is its mid-point. D and E are points on the same side of AB such that angle BAD = angle ABE and angle EPA = angle DPB (see Fig. 7.22). Show that

Fig. 7.21

(6) Delta DAP cong Delta*EBP

(i) AD = BE

E

D

A

P

Fig. 7.22

eq

ناح

8. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM Point D is joined to point B (see Fig. 7.23). Show that:

(1) triangle A MC cong triangle BMD

M

C

(ii) is a right angle. angle DBC

angle 1 +C2+ angle3 angle A Rightarrow LB = LC = 6h 362180 angle 2 = 60 deg angle x +L2+L2=16c

(iii) Delta DBC cong Delta*ACB

Fig. 7.23

(iv) CM = 1/2 * AB
chapter 7, class 9 th, triangles