Advertisements
Advertisements
प्रश्न
Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
Two quadrilaterals are similar, if their corresponding angles are equal and corresponding sides must also be proportional.
APPEARS IN
संबंधित प्रश्न
In the following figure, if LM || CB and LN || CD, prove that `("AM")/("AB")=("AN")/("AD")`
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)`
In ΔPQR, MN is parallel to QR and `(PM)/(MQ) = 2/3`
1) Find `(MN)/(QR)`
2) Prove that ΔOMN and ΔORQ are similar.
3) Find, Area of ΔOMN : Area of ΔORQ
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.
1) Prove ΔABC ~ ΔAMP
2) Find AB and BC.
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 a circle, two chords AB and CD intersect at a point P inside the circle. Prove that
(a) ΔPAC ∼PDB (b) PA. PB= PC.PD
In Figure 3, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. If arcs of equal radii 7 cm have been drawn, with centres A,B, C and D, then find the area of the shaded region.
D and E are points on the sides AB and AC respectively of Δ ABC such that AB=5.6cm, AD= 1.4cm, AC=7 .2cm and AE = 1.5 cm, show that DE is parallel to BC
The scale of a map is 1 : 200000. A plot of land of area 20km2 is to be represented on the map. Find:
The number of kilometres on the ground represented by lcm or the map
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 triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find : A' B', if AB = 4 cm.
In ΔABC, D and E are the points on sides AB and AC respectively. Find whether DE || BC, if:
- AB = 9 cm, AD = 4 cm, AE = 6 cm and EC = 7.5 cm.
- AB = 6.3 cm, EC = 11.0 cm, AD = 0.8 cm and AE = 1.6 cm.
In the figure, given below, PQR is a right-angle triangle right angled at Q. XY is parallel to QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1 : 2. Calculate the lengths of PR and QR.
Choose the correct alternative:
If ΔABC ~ ΔPQR and 4A (ΔABC) = 25 A(ΔPQR), then AB : PQ = ?
In ΔABC, MN is drawn parallel to BC. If AB = 3.5cm, AM : AB = 5 : 7 and NC = 2cm, find:
(i) AM
(ii) AC
The sides PQ and PR of the ΔPQR are produced to S and T respectively. ST is drawn parallel to QR and PQ: PS = 3:4. If PT = 9.6 cm, find PR. If 'p' be the length of the perpendicular from P to QR, find the length of the perpendicular from P to ST in terms of 'p'.
In the figure, PR || SQ. If PR = 10cm, PT = 5cm, TQ = 6cm and ST = 9cm, calculate RT and SQ.
D and E are points on the sides AB and AC of ΔABC such that DE | | BC and divides ΔABC into two parts, equal in area. Find `"BD"/"AB"`.
In ΔABC, AB = 8cm, AC = 10cm and ∠B = 90°. P and Q are the points on the sides AB and AC respectively such that PQ = 3cm ad ∠PQA = 90. Find: Area of quadrilateral PBCQ: area of ΔABC.
Find the scale factor in each of the following and state the type of size transformation:
Actual length = 12cm, Image length = 15cm.
ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate:Length of B' C', if BC = 8cm
Two similar triangles will always have ________ angles
If ∆ABC – ∆PQR in which ∠A = 53° and ∠Q = 77°, then ∠R is
In fig. BP ⊥ AC, CQ ⊥ AB, A−P−C, and A−Q−B then show that ΔAPB and ΔAQC are similar.
In ΔAPB and ΔAQC
∠APB = [ ]° ......(i)
∠AQC = [ ]° ......(ii)
∠APB ≅ ∠AQC .....[From (i) and (ii)]
∠PAB ≅ ∠QAC .....[______]
ΔAPB ~ ΔAQC .....[______]
ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?
ΔDEF ~ ΔABC. If DE : AB = 2 : 3 and ar ΔDEF is equal to 44 square units then ar (ΔABC) (square unit) is ______.
In the given figure, ∠ACB = ∠CDA, AC = 8cm, AD = 3cm, then BD is ______.
ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA.
