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प्रश्न
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:
उत्तर
In ∆ACE and ∆BDE,
∠ACE = ∠BDE ......(AC || BD, alternate interior angles)
CE = DE ......(Given)
∠AEC = ∠BED ......(Vertically opposite angles)
∴ ∆ACE ≅ ∆BDE ......(ASA criterion)
∴ Triangles are congruent but not by RHS congruence criterion
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संबंधित प्रश्न
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, ∠B = 90°, AC = 8 cm, AB = 3 cm.
∆PQR, ∠P = 90°, PR = 3 cm, QR = 8 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?
In the given figure, ∠CIP ≡ ∠COP and ∠HIP ≡ ∠HOP. Prove that IP ≡ OP.
In the given figure, D is the midpoint of OE and ∠CDE = 90°. Prove that ΔODC ≡ ΔEDC
Is ΔPRQ ≡ ΔQSP? Why?
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 figure, QS ⊥ PR, RT ⊥ PQ and QS = RT.
- Is ∆QSR = ∆RTO? Give reasons.
- Is ∠PQR = ∠PRQ? Give reasons.
