English
Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 8

Is ΔPRQ ≡ ΔQSP? Why? - Mathematics

Advertisements
Advertisements

Question

Is ΔPRQ ≡ ΔQSP? Why?

Sum
Advertisements

Solution

In ΔPRQ and ΔPSQ

∠PRQ = ∠PSQ = 90° ...(given)

PR = QS = 3 cm ...(given)

PQ = PQ = 5 cm .......(common)

It satisfies RHS criteria

∴ ΔPRQ congruent to ΔQSP.

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Geometry - Exercise 5.1 [Page 166]

APPEARS IN

Samacheer Kalvi Mathematics [English] Class 8 TN Board
Chapter 5 Geometry
Exercise 5.1 | Q 6 | Page 166

RELATED QUESTIONS

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, using the RHS congruence rule. In the case of congruent triangles, write the result in symbolic form:

∆ABC, ∠A = 90°, AC = 5 cm, BC = 9 cm.

∆PQR, ∠Q = 90°, PR = 8 cm, PQ = 5 cm.


In Fig, DA ⊥ AB, CB ⊥ AB, and AC = BD. State the three pairs of equal parts in ∆ABC and ∆DAB. Which of the following statements is meaningful?


(i) ∆ABC ≅ ∆BAD
(ii) ∆ABC ≅ ∆ABD.


In Fig,

BD and CE are altitudes of ∆ABC such that BD = CE.
(i) State the three pairs of equal parts in ∆CBD and ∆BCE.
(ii) Is ∆CBD ≅ ∆BCE? Why or why not?
(iii) Is ∠DCB = ∠EBC? Why or why not?


ABC is an isosceles triangle with AB = AC and AD is one of its altitudes.


(i) State the three pairs of equal parts in ∆ADB and ∆ADC.
(ii) Is ∆ADB ≅ ∆ADC? Why or why not?
(iii) Is ∠B = ∠C? Why or why not?
(iv) Is BD = CD? Why or why not?


State whether the two triangles are congruent or not. Justify your answer


To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion


In the given pairs of triangles of the figure, using only RHS congruence criterion, determine which pairs of triangles are congruent. In congruence, write the result in symbolic form:


In the given pairs of triangles of the figure, using only RHS congruence criterion, determine which pairs of triangles are congruent. In congruence, write the result in symbolic form:


In the given pairs of triangles of the figure, using only RHS congruence criterion, determine which pairs of triangles are congruent. In congruence, write the result in symbolic form:


In the following figure, QS ⊥ PR, RT ⊥ PQ and QS = RT.

  1. Is ∆QSR = ∆RTO? Give reasons.
  2. Is ∠PQR = ∠PRQ? Give reasons.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×