Advertisements
Advertisements
Question
In the following figure, QS ⊥ PR, RT ⊥ PQ and QS = RT.
- Is ∆QSR = ∆RTO? Give reasons.
- Is ∠PQR = ∠PRQ? Give reasons.
Advertisements
Solution
i. In ∆QSR and ∆RTQ,
∠QSR = ∠RTQ = 90° ...(∵ QS ⊥ PR and RT ⊥ PQ (given))
QS = RT ...(Given)
QR = RQ ...(Common hypotenuse)
∴ ∆QSR ≅ ∆RTQ ...(RHS criterion)
ii. Yes, by using (i) part, we get
∠TQR = ∠SRQ ...(By C.P.C.T)
⇒ ∠PQR = PRQ
APPEARS IN
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, ∠B = 90°, AC = 8 cm, AB = 3 cm.
∆PQR, ∠P = 90°, PR = 3 cm, QR = 8 cm.
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.
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.
Is ΔPRQ ≡ ΔQSP? Why?
State whether the two triangles are congruent or not. Justify your answer
For the given pair of triangles state the criterion that can be used to determine the congruency?
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:
