CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

ABC with verticesA(-2,0),B(2,0) andC(0,2) is similar to DEF with vertices D(-4,0)E(4,0) and F(0,4). State whether the following statement is true or false. Justify your answer.


A
True
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
False
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A True

Step 1: Find the length of sides of ABC

We know that Distance formula,d=(x2x1)2+(y2y1)2

In triangle ABC

by applying the distance formula

AB=((2-(-2))2+0=(2+2)2=42=16=4

BC=(0-2)2+(2-0)2=4+4=22

CA=(-2-0)2+(0-2)2=4+4=22

Step 2: Find the length of sides of DEF

Now in DEF

DE=(4-(-4))2+0=(4+4)2=64=8

EF=(0-4)2+(4-0)2=16+16=42

FD=(-4-0)2+(0-4)2=16+16=42

Step 2: Find the ratio of corresponding sides

we have the ratio of corresponding sides of the triangle ,

ABDE=BCEF=CAFD=12

ΔABC~ΔDEF

Hence, triangle ABC andDEF are similar.


flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image