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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Write the test of similarity for triangles given in figure. - Geometry Mathematics 2

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प्रश्न

Write the test of similarity for triangles given in figure.

बेरीज

उत्तर

In ΔABC and ΔPQR

∠ABC ≅ ∠PQR      ......[Each of measure 60°]

∠ACB ≅ ∠PRQ      ......[Each of measure 30°]

∴ ΔABC ~ ΔPQR     ......[AA test of similarity]

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Similarity - Q.1 (B)

संबंधित प्रश्‍न

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}.`


See the given figure. DE || BC. Find EC.


Given `triangle ABC ~ triangle PQR`, if `(AB)/(PQ) = 1/3`, then find `(ar  triangle ABC)/(ar triangle PQR)`


In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm.

  1. Prove that ΔACD is similar to ΔBCA.
  2. Find BC and CD.
  3. Find area of ΔACD : area of ΔABC.


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.


In triangle ABC, AD is perpendicular to side BC and AD2 = BD × DC. Show that angle BAC = 90°.


In the given figure, QR is parallel to AB and DR is parallel to AB and DR is parallel to QB.


Prove that: PQ2 = PD × PA.


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 the following figure, point D divides AB in the ratio 3 : 5. Find : `(AD)/(AB)`


In the given figure, ΔABC ~ ΔADE. If AE : EC = 4 : 7 and DE = 6.6 cm, find BC. If 'x' be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of 'x'. 


The given figure shows a parallelogram ABCD. E is a point in AD and CE produced meets BA produced at point F. If AE = 4 cm, AF = 8 cm and AB = 12 cm, find the perimeter of the parallelogram ABCD.


D and E are points on the sides AB and AC respectively of a Δ ABC such that DE | | BC and divides Δ ABC into two parts, equal in area. Find `"BD"/"AB"`.


ABCD is a parallelogram whose sides AB and BC are 18cm and 12cm respectively. G is a point on AC such that CG : GA = 3 : 5 BG is produced to meet CD at Q and AD produced at P. Prove that ΔCGB ∼ ΔAGP. Hence, fi AP.


AM and DN are the altitudes of two similar triangles ABC and DEF. Prove that: AM : DN = AB : DE.


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


ΔABC is enlarged, with a scale factor 5. Find: BC, f B'C' = 16cm


Construct a triangle similar to a given triangle ABC with its sides equal to `6/5` of the corresponding sides of the triangle ABC (scale factor `6/5 > 1`)


Which of the following is not a test of similarity?


Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.


In the adjoining diagram the length of PR is ______.


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