ASA Congruence Rule Application
We are given two triangles, $\Delta LMN$ and $\Delta OPQ$.
The following conditions are met:
- Angle Equality: $\angle L = \angle O$
- Side Equality: $LM = OP$
- Angle Equality: $\angle M = \angle P$
The side $LM$ in $\Delta LMN$ connects vertex $L$ and vertex $M$. This side is included between the angles $\angle L$ and $\angle M$. Similarly, the side $OP$ in $\Delta OPQ$ is included between the angles $\angle O$ and $\angle P$.
The Angle-Side-Angle (ASA) congruence postulate states that if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the two triangles are congruent.
Since we have established that $\angle L = \angle O$, the included side $LM = OP$, and $\angle M = \angle P$, the ASA congruence rule applies directly.
Therefore, $\Delta LMN \cong \Delta OPQ$ by the ASA rule.
Similar Questions
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Important Questions from Triangles, Congruence and Similarity
Angle between the internal bisectors of two angles ∠B and ∠C of a ΔABC is 132°, then the value of ∠A is
In ΔPQR, PQ = PR and S is a point on QR such that ∠PSQ = 96° + ∠QPS and ∠QPR = 132°. What is the measure of ∠PSR?
In Δ ABC, ∠A = 50°. If the bisectors of the angle B and angle C, meet at a point O, then ∠BOC is equal to:
Triangle ABC is right angled at B. BD is an altitude intersecting AC at D. If AC = 9 cm and CD = 3 cm. then find the measure of AB (in cm).
The base and altitude of an isosceles triangle are 10 cm and 12 cm respectively. Then the length of each equal side is:
