मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता ९ वी

In the given figure, ∠P ≅ ∠R seg, PQ ≅ seg RQ. Prove that, ΔPQT ≅ ΔRQS.

Advertisements
Advertisements

प्रश्न

In the given figure, ∠P ≅ ∠R seg, PQ ≅ seg RQ. Prove that, ΔPQT ≅ ΔRQS.

बेरीज
Advertisements

उत्तर

In △PQT and △RQS

∠P = ∠R         ...(Given)

seg PQ = seg RQ         ...(Given)

∠Q = ∠Q           ...(Common)

△PQT ≅ △RQS      ...(ASA test)

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Triangles - Practice Set 3.2 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics 2 [English] Standard 9 Maharashtra State Board
पाठ 3 Triangles
Practice Set 3.2 | Q 6. | पृष्ठ ३३

संबंधित प्रश्‍न

CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ΔADE ≅ΔBCE.


ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true:


Which of the following is not a criterion for congruence of triangles?


If ABC and DEF are two triangles such that ΔABC \[\cong\] ΔFDE and AB = 5cm, ∠B = 40°


In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC =  5 cm, then CD =


From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.


In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?


If the following pair of the triangle is congruent? state the condition of congruency : 
In  ΔABC and ΔDEF,  ∠B = ∠E = 90o; AC = DF and BC = EF.


In the following diagram, ABCD is a square and APB is an equilateral triangle.

(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.


In the following diagram, AP and BQ are equal and parallel to each other. 

Prove that:  

  1. ΔAOP ≅ ΔBOQ.
  2. AB and PQ bisect each other.

State, whether the pairs of triangles given in the following figures are congruent or not:

Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.


Prove that:

  1. ∆ ABD ≅ ∆ ACD
  2. ∠B = ∠C
  3. ∠ADB = ∠ADC
  4. ∠ADB = 90°


Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).


Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).


Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).


In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.


In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.


In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.


Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.


The congruent figures super impose each other completely.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×