Question

PQR and XYZ are similar right angled triangles.

A) work out the length of XY
Note:your finial line should say "XY=...."
(2 marks)
Rectangles ABCD and DEFG are congruent.
AB= 7cm
AD=3AB
B) work out the length of CE.
Note your final line should say "CE=..."
(2 marks).
​

Answer 1

XY=4

CE=14

Explanation:

A)since the 2 traingles are similar, there is a ratio between the 2 of them. we can find that by dividing the side :10/25 =0.4. so XYZ is 0.4 of PQR. to check that we can try to multiply pr by 0.4 to see if it gets XZ. 25 • 0.4 =10.To get XY we will do the same thing: PQ • 0.4 = 10 • 0.4 = 4

B)AB= 7

CD= AB =7

AD = 3 AB

AD = 3•7

AD= 21

Since ABCD is congruent to DEFG

AD =ED = 21

CE = ED-CD = 21-7=14

Answer 2

1. 4cm

2. 14cm

Explanation:

Similarity

Two shapes are similar if and only if the ratio of their corresponding sides are equal. That is, the ratio of their bases is equal to the ratio of their heights is equal to the ratio of their hypotenuses.

Congruence

If two shapes are said to be congruent, that means they are exacrly the same:same shape and same size

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

If ΔPQR and ΔXYZ are similar,

`(PQ)/(XY)=(QR)/(YZ)=(PR)/(XZ)`

`(25)/(10)=(10)/(XY)`

`25XY = 10(10) = 100`

`XY = (100)/(25) = 4`

`\:`

If ABCD and DEFG are congruent,

AB=EF=CD=DG and BC=ED=AD=FG.

We have AB=CD=7 and AD=DE=21.

CE=DE-CD=21-7=14cm