Everything Maths Grade 11

16.4 CHAPTER 16. GEOMETRY

Example 4: Triangle Geometry 1

QUESTION

In�GHI, GH� LJ; GJ� LK andJKKI=^53. DetermineHJKI.

SOLUTION

G

H

I

J

K

L

Step 1 : Identify similar triangles

LIJˆ = GIHˆ

JLIˆ = HGIˆ (Corresponding∠’s)

∴�LIJ|||�GIH (Equiangular�’s)

LIKˆ = GIJˆ

KLIˆ = JGIˆ (Corresponding∠’s)

∴�LIK|||�GIJ (Equiangular�’s)

Step 2 : Use proportional sides

HJ

JI

=

GL

LI

(�LIJ|||�GIH)

and

GL

LI

=

JK

KI

(�LIK|||�GIJ)

=

5

3

∴

HJ

JI

=

5

3

Step 3 : Rearrange to find the required ratio

HJ

KI

=

HJ

JI

×

JI

KI