मराठी

State the Sas-similarity Criterion - Mathematics

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प्रश्न

State the SAS-similarity criterion 

उत्तर

If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional then the two triangles are similar

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पाठ 4: Triangles - Exercises 5

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संबंधित प्रश्‍न

In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD.


P and Q are points on sides AB and AC respectively of ∆ABC. If AP = 3 cm, PB = 6cm. AQ = 5 cm and QC = 10 cm, show that BC = 3PQ.


In ∆ABC, DE is parallel to base BC, with D on AB and E on AC. If `\frac{AD}{DB}=\frac{2}{3}` , find `\frac{BC}{DE}.`


In the following figure, DE || OQ and DF || OR, show that EF || QR.


ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that `("AO")/("BO") = ("CO")/("DO")`


The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle?


Given: ∠GHE = ∠DFE = 90°,

DH = 8, DF = 12,

DG = 3x – 1 and DE = 4x + 2.


Find: the lengths of segments DG and DE.


Given: FB = FD, AE ⊥ FD and FC ⊥ AD.

Prove that: `(FB)/(AD) = (BC)/(ED)`.


The perimeter of two similar triangles are 30 cm and 24 cm. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle.


The given figure shows a triangle PQR in which XY is parallel to QR. If PX : XQ = 1 : 3 and QR = 9 cm, find the length of XY.


Further, if the area of ΔPXY = x cm2; find, in terms of x the area of :

  1. triangle PQR.
  2. trapezium XQRY.

In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ΔADE and the trapezium BCED. 

 


In ∆ABC, AP ⊥ BC, BQ ⊥ AC B– P–C, A–Q – C then prove that, ∆CPA ~ ∆CQB. If AP = 7, BQ = 8, BC = 12 then Find AC. 


∆ABC and ∆DEF are equilateral triangles, A(∆ABC): A(∆DEF) = 1: 2. If AB = 4 then what is length of DE? 


Figure shows Δ KLM , P an T on KL and KM respectively such that∠ KLM =∠ KTP. 

If `"KL"/"KT" = 9/5` , find `("Ar" triangle "KLM")/("Ar" triangle "KTP")`.


The dimensions of a buiIding are 50 m Iong, 40m wide and 70m high. A model of the same building is made with a scale factor of 1: 500. Find the dimensions of the model.


A ship is 400m laig and 100m wide. The length of its model is 20 cm. find the surface area of the deck of the model. 


A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate: the length of LM, if L' M' = 5.4 cm.


In ΔABC, D and E are the points on sides AB and AC respectively. Find whether DE || BC, if:

  1. AB = 9 cm, AD = 4 cm, AE = 6 cm and EC = 7.5 cm.
  2. AB = 6.3 cm, EC = 11.0 cm, AD = 0.8 cm and AE = 1.6 cm.

If ΔABC ~ ΔDEF, then writes the corresponding congruent angles and also write the ratio of corresponding sides. 


Equilateral triangles are drawn on the sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.


On a map drawn to scale of 1 : 2,50,000 a rectangular plot of land ABCD has the following measurement AB = 12 cm, BC = 16 cm angles A, B, C, and D are 900 each. Calculate:
(i) The diagonal distance of the plot of land in
(ii) Actual length of diagonal.


In ΔABC, DE is parallel to BC and DE = 3:8.

Find:
(i) AD : BD
(ii) AE, if AC = 16.


In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"EC"`


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.


Find the scale factor in each of the following and state the type of size transformation:
Actual length = 12cm, Image length = 15cm.


In the adjacent figure ∠BAC = 90° and AD ⊥ BC then
 


In given fig., quadrilateral PQRS, side PQ || side SR, AR = 5 AP, then prove that, SR = 5PQ


In the figure PQ || BC. If `"PQ"/"BC" = 2/5` then `"AP"/"PB"` is ______.


In ΔABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.


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.


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