Mathematics

In the figure given below, $AB, EF$ and $CD$ are parallel lines. Given that $AB =15\ cm, EG = 5\ cm, GC = 10\ cm$ and $DC = 18 cm$. Calculate(i) $EF$(ii) $AC$.

SOLUTION
Consider $\triangle EFG$ and $\triangle GCD$
$EF\parallel CD\implies \angle GCD=\angle GEF\ (\because$ alternative angles $)$
$\angle FGE=\angle CGD\ (\because$ vertically opposite angles $)$
as two angles are equal automatically third angle will be equal
So by AAA criteria , we get
$\triangle EFG\sim \triangle CDG$
$\implies \dfrac{EF}{EG}=\dfrac{CG}{CD}\implies EF=5\times \dfrac{18}{10}=9\ cm$
$AB\parallel EF\implies \angle BAC=\angle FEC,\angle ABC=\angle EFC$ and $\angle C$ remains the same
So by AAA criteria ,we get
$\triangle ABC\sim \triangle EFC$
$\implies \dfrac{AC}{AB}=\dfrac{EC}{EF}\implies AC=15\times \dfrac{15}{9}=25\ cm$

You're just one step away

Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

Realted Questions

Q1 Subjective Medium
Look at the pictures. Mark the angles and colour them as indicated below.
(a) If the angle is right angle then mark it in blue.
(b) If an angle is less than a right angle then mark it in red.
(c) If an angle is more than a right angle then mark it in black.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 One Word Medium
Fill in the blanks:
Two different lines in a plane either ...... at exactly one point or are parallel.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Subjective Medium
Two straight lines AB and CD intersect each other at a point O and angle $AOC = 50^\circ,$ find:
$\angle BOC$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
In the adjoining figure, identify the vertically opposite angles.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
List three other situations where reflex angles may be seen.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020