Advertisements
Advertisements
Question
Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.
Options
True
False
Solution
This statement is False.
Explanation:
Two quadrilaterals are similar, if their corresponding angles are equal and corresponding sides must also be proportional.
APPEARS IN
RELATED QUESTIONS
Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD.
In figure, `\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}` and AB = 5 cm. Find the value of DC.
Prove that the line segments joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle
In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm.
- Prove that ΔACD is similar to ΔBCA.
- Find BC and CD.
- Find area of ΔACD : area of ΔABC.
State, true or false:
All isosceles triangles are similar.
Given: ∠GHE = ∠DFE = 90°,
DH = 8, DF = 12,
DG = 3x – 1 and DE = 4x + 2.
Find: the lengths of segments DG and DE.
Area of two similar triangles are 98 sq. cm and 128 sq. cm. Find the ratio between the lengths of their corresponding sides.
A line PQ is drawn parallel to the base BC of ∆ABC which meets sides AB and AC at points P and Q respectively. If AP = `1/3` PB; find the value of:
- `"Area of ΔABC"/"Area of ΔAPQ"`
- `"Area of ΔAPQ"/"Area of trapezium PBCQ"`
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:
In ΔPQR, PQ = 10 cm, QR = 12cm, PR = 8 cm, find the biggest and the smallest angle of the triangle.
Prove that the area of Δ BCE described on one side BC of a square ABCD is one half the area of the similar Δ ACF described on the diagonal AC.
In Δ ABC, DE || BC; DC and EB intersects at F. if `"DE"/"BC" = 2/7` , find `("Ar" (triangle "FDE"))/("Ar" (triangle "FBC"))`
In the figure , ABCD is a quadrilateral . F is a point on AD such that AF = 2.1 cm and FD = 4.9 cm . E and G are points on AC and AB respectively such that EF || CD and GE || BC . Find `("Ar" triangle "BCD")/("Ar" triangle "GEF")`
Δ ABC ∼ Δ PQR such that AB= 1.5 cm and PQ=2. 1 cm. Find the ratio of areas of Δ ABC and ΔPQR.
In the given figure, PQ || AB; CQ = 4.8 cm QB = 3.6 cm and AB = 6.3 cm. Find : PQ
Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are `3/5` of the corresponding sides of the first triangle.
Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.
In the adjoining figure. BC is parallel to DE, area of ΔABC = 25 sq cm, area of trapezium BCED = 24 sq cm, DE = 14 cm. Calculate the length of BC.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 8cm, AB = 12cm and AE = 12cm, find CE.
Through the vertex S of a parallelogram PQRS, a line is drawn to intersect the sides Qp and QR produced at M and N respectively. Prove that `"SP"/"PM" = "MQ"/"QN" = "MR"/"SR"`
Harmeet is 6 feet tall and casts a shadow of 3 feet long. What is the height of a nearby pole if it casts a shadow of 12 feet long at the same time?
The dimensions of the model of a building are 1.2m x 75cm x 2m. If the scale factor is 1 : 20; find the actual dimensions of the building.
A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The volume of the model if the volume of the truck is 6m3
A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower
In the adjacent figure ∠BAC = 90° and AD ⊥ BC then
ΔABC ~ ΔDEF. Write the ratios of their corresponding sides
In ΔABC, AP ⊥ BC and BQ ⊥ AC, B−P−C, A−Q−C, then show that ΔCPA ~ ΔCQB. If AP = 7, BQ = 8, BC = 12, then AC = ?
In ΔCPA and ΔCQB
∠CPA ≅ [∠ ______] ...[each 90°]
∠ACP ≅ [∠ ______] ...[common angle]
ΔCPA ~ ΔCQB ......[______ similarity test]
`"AP"/"BQ" = (["______"])/"BC"` .......[corresponding sides of similar triangles]
`7/8 = (["______"])/12`
AC × [______] = 7 × 12
AC = 10.5
ΔDEF ~ ΔABC. If DE : AB = 2 : 3 and ar ΔDEF is equal to 44 square units then ar (ΔABC) (square unit) is ______.
∆ABC ~ ∆PQR. If AM and PN are altitudes of ΔABC and ∆PQR respectively and AB2 : PQ2 = 4 : 9, then AM : PN = ______.
