English

In Triangles Abc and Pqr Three Equality Relations Between Some Parts Are as Follows: Ab = Qp, ∠B = ∠P and Bc = Pr - Mathematics

Advertisements
Advertisements

Question

In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ∠B = ∠P and BC = PR

State which of the congruence conditions applies:

Options

  •  SAS

  • ASA

  • SSS

  • RHS

MCQ
Advertisements

Solution

In  Δ ABC and Δ PQR 

It is given that

AB = QP

∠B = ∠P

BC = PR

Since two sides and an angle are equal so it obeys  SAS

Hence (a) SAS

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Congruent Triangles - Exercise 12.8 [Page 85]

APPEARS IN

RD Sharma Mathematics [English] Class 9
Chapter 12 Congruent Triangles
Exercise 12.8 | Q 4 | Page 85

RELATED QUESTIONS

In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.


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


In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is


In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.

 By ______ test

ΔXYZ ≅ ΔLMN


Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

From the information shown in the figure,

in ΔPTQ and ΔSTR

seg PT ≅ seg ST

∠PTQ ≅ ∠STR        ...[Vertically opposite angles]

∴ ΔPTQ ≅ ΔSTR       ...`square` test

∴ `{:("∠TPQ" ≅ square),("and"  square ≅ "∠TRS"):}}`      ...corresponding angles of congruent triangles

seg PQ ≅ `square`         ...corresponding sides of congruent triangles


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;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).


In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.


∆ABC and ∆PQR are congruent under the correspondence:
ABC ↔ RQP
Write the parts of ∆ABC that correspond to
(i) `bar"PQ"`
(ii)∠Q
(iii) `bar"RP"`


Two figures are congruent, if they have the same shape.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×