Advertisements
Advertisements
Question
In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: ΔAOB is similar to ΔCOD.
Solution
Since AO = 2CO and BO = 2DO,
`(AO)/(CO) = 2/1 = (BO)/(DO)`
Also, ∠AOB = ∠DOC ...(Vertically opposite angles)
So, ΔAOB ∼ ΔCOD ...(SAS criterion for similarity)
APPEARS IN
RELATED QUESTIONS
In quadrilateral ABCD, diagonals AC and BD intersect at point E such that
AE : EC = BE : ED. Show that: ABCD is a trapezium.
Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, prove that : `(AB)/(PQ) = (AD)/(PM)`.
In the figure given below, AB ‖ EF ‖ CD. If AB = 22.5 cm, EP = 7.5 cm, PC = 15 cm and DC = 27 cm. Calculate : AC
In the given figure, AB and DE are perpendiculars to BC.
If AB = 6 cm, DE = 4 cm and AC = 15 cm. Calculate CD.
Triangles ABC and DEF are similar.
If area (ΔABC) = 9 cm2, area (ΔDEF) = 64 cm2 and DE = 5.1 cm, find AB.
Triangles ABC and DEF are similar.
If AC = 19 cm and DF = 8 cm, find the ratio between the area of two triangles.
In the adjoining figure, ΔACB ∼ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm find the area (∆ACB) : area (∆APQ).
On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90°.
Calculate:
- the actual lengths of AB and BC in km.
- the area of the plot in sq. km.
In the given figure ΔABC and ΔAMP are right angled at B and M respectively.
Given AC = 10 cm, AP = 15 cm and PM = 12 cm.
(i) Prove ΔABC ∼ Δ AMP.
(ii) Find AB and BC.
Triangles ABC and DEF are similar.
If AC = 19 cm and DF = 8 cm, find the ratio between the areas of two triangles.
