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
- In an urban project, triangular plots with side ratios 3:4:5 are allocated. If the perimeter is 60 m, find the area.
- In $\Delta ABC \sim \Delta XYZ$ and $AB = 4 \text{ cm}, BC = 6 \text{ cm}, XY = 8 \text{ cm}$, what is the length of YZ?
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- In triangle ABC, DE is drawn parallel to BC, intersecting AB and AC at D and E respectively. If AD=3, DB=6, and AE=4, find EC.
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Important Questions from Triangles, Congruence and Similarity
The radius of the circumcircle of an equilateral triangle of √3 unit side, is:
If the ratio of the angles of a triangle is 3 : 5 : 7, find the value of the largest angle.
A. 36°
B. 60°
C. 84°
D. 15°
If ΔABC and Δ PQR are similar and \(\rm\frac{BC}{QR} = \frac{1}{3}\) , find \(\rm\frac{ar(\Delta PQR)} {ar(\Delta BCA)}\)
If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the smallest angle.
ABCD is a parallelogram. Side BC is produced to E such that BC = CE. Join AE which intersects side CD at P. The area of triangle ABE is:
