In triangle ABC and NML, BL is perpendicular to AC, MC is perpendicular to LN, AL =CN and BL=CM - Maths - Triangles

Question

In triangle ABC and NML, BL is perpendicular to AC, MC is
perpendicular to LN, AL =CN and BL=CM Prove that triangle ABC is
congruent to triangle NML

Pronay · Accepted Answer

Given : BL is perpendicular to AC and MC is perpendicular to LN. AL=CN and BL=CM

In ΔABL and ΔNMC

AL=CN

∠ALB=∠NCM= $90^{\circ}$

BL=CM

Therefore ΔABL $≅$ ΔNMC (by SAS rule)

AB=NM ( CPCT)

∠BAL=∠MNC (CPCT)

AL=CN ⇒ AL+LC=LC+CN⇒AC=LN

Now in ΔABC and ΔNML

AB=NM

∠BAC=∠MNL

AC=LN

Therefore ΔABC $≅$ ΔNML (by SAS rule)

In triangle ABC and NML, BL is perpendicular to AC, MC is perpendicular to LN, AL =CN and BL=CM. Prove that triangle ABC is congruent to triangle NML.