Advertisements
Advertisements
प्रश्न
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
ΔADE ~ ΔACB.
उत्तर
In ΔADE and ΔACB.
∠AED = ∠ABC ...(both are right angles)
∠DAE = ∠CAB ....(common angles)
ΔADE ∼ ΔACB ...(AA criterion for similarity)
APPEARS IN
संबंधित प्रश्न
In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: If BD = 2.4 cm, AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and PC.
Angle BAC of triangle ABC is obtuse and AB = AC. P is a point in BC such that PC = 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ = 15 cm and PR = 9 cm; find the length of PB.
In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm.
Find :
- `(AY)/(YC)`
- `(YC)/(AC)`
- XY
In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm.
Find : `(YC)/(AC)`
In the following figure, ABCD to a trapezium with AB ‖ DC. If AB = 9 cm, DC = 18 cm, CF = 13.5 cm, AP = 6 cm and BE = 15 cm, Calculate: PE
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 :
- EF
- AC
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.
Prove that : ΔABC ~ ΔDEC
Triangles ABC and DEF are similar.
If area (ΔABC) = 36 cm2, area (ΔDEF) = 64 cm2 and DE = 6.2 cm, find AB.
Triangles ABC and DEF are similar.
If area (ΔABC) = 16 cm2, area (ΔDEF) = 25 cm2 and BC = 2·3 cm find EF.
