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

In the Figure, Parts of the Two Triangles Bearing Identical Marks Arecongruent. State the Test by Which the Triangles Are Congruent. - Geometry Mathematics 2

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प्रश्न

In the figure, parts of the two triangles bearing identical marks are
congruent. State the test by which the triangles are congruent.

उत्तर

Δ ABC and ΔPQR are congruent by hypotenuse side test.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Balbharati Model Question Paper Set 2

संबंधित प्रश्‍न

In an isosceles ∆ABC, the base AB is produced both ways in P and Q such that AP × BQ = AC2 and CE are the altitudes. Prove that ∆ACP ~ ∆BCQ.


In ΔABC and ΔDEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE=10cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL: DM.


In the given figure, ∆ABC and ∆AMP are right angled at B and M respectively.

Given AC = 10 cm, AP = 15 cm and PM = 12 cm.

  1. Prove that: ∆ABC ~ ∆AMP
  2. Find: AB and BC.


In the given figure, AB || EF || DC; AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm.

  1. Name the three pairs of similar triangles.
  2. Find the lengths of EC and EF.

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, ΔOAB ~ ΔOCD. If AB = 8cm, BO = 6.4cm, OC = 3.5cm and CD = 5cm, find (i) OA (ii) DO.  


ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.  

 


In the given figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and AC is 14 cm. If arcs of equal radii 7 cm taking A, B, C and D as centres, have been drawn, then find the area of the shaded region ?


A model of a ship is made with a scale factor of 1 : 500. Find 

The volume of the ship, if the volume of its model is 200 cm3.  


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


A line PQ is drawn parallel to the side BC of ΔABC which cuts side AB at P and side AC at Q. If AB = 9.0 cm, CA = 6.0 cm and AQ = 4.2 cm, find the length of AP.


In the following figure, M is mid-point of BC of a parallelogram ABCD. DM intersects the diagonal AC at P and AB produced at E. Prove that : PE = 2 PD 


If ΔPQR, AB is drawn parallel to QR. If PQ = 9cm, PR = 6cm and PB = 4.cm, find the length of AP.


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


A plot of land of area 20km2 is represented on the map with a scale factor of 1:200000. Find: The area on the map that represented the plot of land.


In the adjacent figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ


In the given figure, UB || AT and CU ≡ CB Prove that ΔCUB ~ ΔCAT and hence ΔCAT is isosceles.


Observe the figure and complete the following activity


In fig, ∠B = 75°, ∠D = 75°

∠B ≅ [ ______ ]       ...[each of 75°]

∠C ≅ ∠C         ...[ ______ ]

ΔABC ~ Δ [ ______ ]     ...[ ______ similarity test]


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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