Advertisements
Advertisements
प्रश्न
In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form:
उत्तर
We have :
`(DE)/(QR)=2.5/5=1/2`
`(EF)/(PQ)=2/4=1/2`
`(DF)/(PR)=3/6=1/2`
⇒` (DE)/(QR)=(EF)/(PQ)=(DF)/(PR)`
Therefore, by SSS similarity theorem, Δ FED- Δ PQR
APPEARS IN
संबंधित प्रश्न
The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Prove that DF × EF = FB × FA
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL
E and F are points on the sides PQ and PR, respectively, of a ΔPQR. For the following case, state whether EF || QR:
PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
In the following figure, seg DH ⊥ seg EF and seg GK ⊥ seg EF. If DH = 18 cm, GK = 30 cm and `A(triangle DEF) = 450 cm^2`, then find:
1) EF
2) `A(triangle GFE)`
3) `A(square DFGE)`
The given diagram shows two isosceles triangles which are similar. In the given diagram, PQ and BC are not parallel; PC = 4, AQ = 3, QB = 12, BC = 15 and AP = PQ.
Calculate:
- the length of AP,
- the ratio of the areas of triangle APQ and triangle ABC.
In the given triangle P, Q and R are the mid-points of sides AB, BC and AC respectively. Prove that triangle PQR is similar to triangle ABC.
In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1cm, PB = 3cm, AQ = 1.5cm, QC = 4.5cm, prove that area of ΔAPQ is 116 of the area of ΔABC.
In Δ ABC , MN || BC .
If `"AB"/"AM" = 9/4` , find `("Ar" ("trapezium MBCN"))/("Ar" . (triangle "ABC"))`
In Δ ABC, DE || BC; DC and EB intersects at F. if `"DE"/"BC" = 2/7` , find `("Ar" (triangle "FDE"))/("Ar" (triangle "FBC"))`
A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate: the length of M' N', if MN = 8 cm.
A model of an aeroplane is made to a scale of 1 : 400. Calculate : the length, in cm, of the model; if the length of the aeroplane is 40 m.
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 ∠ABC = 90°.
Calculate : the actual lengths of AB and BC in km.
In the figure, given below, AB, CD and EF are parallel lines. Given AB = 7.5 cm, DC = y cm, EF = 4.5 cm, BC = x cm and CE = 3 cm, calculate the values of x and y.
Sides of a triangle are 7, 24 and 25. Determine whether the triangle is a right-angled triangle or not.
Prove that the external bisector of an angle of a triangle divides the opposite side externally n the ratio of the sides containing the angle.
PQ is perpendicular to BA and BD is perpendicular to AP.PQ and BD intersect at R. Prove that ΔABD ∼ ΔAPQ and `"AB"/"AP" = "BD"/"PQ"`.
In a right-angled triangle ABC, ∠B = 90°, P and Q are the points on the sides AB and AC such as PQBC, AB = 8 cm, AQ = 6 cm and PA:AB = 1:3. Find the lengths of AC and BC.
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.
A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The length of the truck
A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The base area of the truck, if the base area of the model is 30m2
On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The diagonal distance of the plot in km
Check whether the triangles are similar and find the value of x
D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that b2 = `"p"^2 + "a"x + "a"^2/4`
In the given figure, if ΔEAT ~ ΔBUN, find the measure of all angles.
In the given figure, UB || AT and CU ≡ CB Prove that ΔCUB ~ ΔCAT and hence ΔCAT is isosceles.
If ΔABC ~ ΔLMN and ∠B = 40°, then ∠M = ? Give reason.
In the given figure ΔABC ~ ΔPQR. The value of x is
 |
 |
In the adjoining diagram the length of PR is ______.
