Everything Maths Grade 11

CHAPTER 16. GEOMETRY 16.4

We need to calculateKIJI: We were givenJKKI =^53 So rearranging, we have

JK =^53 KI And:

JI = JK + KI

=

5

3

KI + KI

=

8

3

KI

JI

KI

=

8

3

Using this relation:

=

5

3

×

8

3

=

40

9

Example 5: Triangle Geometry 2

QUESTION

P QRS is a trapezium, with P Q� RS.

Prove that P T. T R = ST. T Q.

1

2

1

(^11)
2 2
2
T
P Q
R S
SOLUTION
Step 4 : Identify similar triangles
Pˆ 1 = Sˆ 1 (alternate∠’s)
Qˆ 1 = Rˆ 1 (alternate∠’s)
∴�P T Q|||�ST R (equiangular�’s)
Step 5 : Use proportional sides

P T

T Q

=

ST

T R

(�P T Q|||�ST R)

∴ P T. T R = ST. T Q