GCSE Similar Shapes

1.	

	BE is parallel to CD.
AE = 6 cm, ED = 4 cm, AB = 4.5 cm, BE = 4.8 cm.
(a)	Calculate the length of CD.
(2)
(b)	Calculate the perimeter of the trapezium EBCD.
(2)
(Total 4 marks)
2.	

	BE is parallel to CD.
ABC and AED are straight lines.
AB = 4 cm, BC = 6 cm, BE = 5 cm, AE = 4.8 cm.
(a)	Calculate the length of CD.
(2)
(b)	Calculate the length of ED.
(2)
(Total 4 marks)

3.	

	BE is parallel to CD.
	AB = 9 cm, BC = 3 cm, CD = 7 cm, AE = 6 cm.
	Calculate the length of ED.
(Total 2 marks)
4.	

	BE is parallel to CD.
	AB = 9 cm, BC = 3 cm, CD = 7 cm, AE = 6 cm.
(a)	Calculate the length of ED.
(2)
(b)	Calculate the length of BE.
(2)
(Total 4 marks)

5.	

	AB is parallel to DE.
ACE and BCD are straight lines.
AB = 6 cm,
AC = 8 cm,
CD = 13.5 cm,
DE = 9 cm.
(i)	Work out the length of CE.
(ii)	Work out the length of BC.
(Total 3 marks)
6.	Shapes ABCD and EFGH are mathematically similar.

Diagrams NOT accurately drawn
(a)	Calculate the length of BC.
(2)
(b)	Calculate the length of EF.
(2)
(Total 4 marks)

7.	

Diagram NOT accurately drawn
	AB is parallel to XY.
The lines AY and BX intersect at P.
AB = 6 cm.
XP = 12.5 cm.
XY = 15 cm.
	Work out the length of BP.
(Total 3 marks)
8.	

Diagram NOT
accurately drawn
	ACQ and BCP are straight lines.
AB is parallel to PQ.
AB = 2 cm.
AC = 3 cm.
CQ = 12 cm.
CP = 10 cm.

(a)	Work out the length of PQ.
(2) 
(b)	Work out the length of BP.
(3)
(Total 5 marks)
9.	
Diagrams NOT accurately drawn

	The two triangles ABC and PQR are mathematically similar.
	Angle A = angle P.
Angle B = angle Q.
AB = 8 cm.
AC = 26 cm.
PQ = 12 cm.
QR = 45 cm.
(a)	Work out the length of PR.
(2)
(b)	Work out the length of BC.
(2)
(Total 4 marks)
10.	

	ABC is an equilateral triangle.
AD is the perpendicular bisector of BC.
BX is the angle bisector of angle ABC.
(a)	Show that triangle BXD is similar to triangle ACD.
(2)
	In triangle ACD,
AC = 2 cm,
AD =  Ö3 cm.
(b)	Show that 
(3)
(Total 5 marks)