Question

<krj and <lrj are right angles
jk = jl
prove: kr = lr
mark everything in the picture first!
what you know
how you know it
<krj and <lrj are right angles
given
jk = lr
given
kr = lr
δkjr ≅ δljr
kr = lr

Explanation:

Step1: Identify the triangles

We have two right - angled triangles \(\triangle KJR\) and \(\triangle LJR\).

Step2: List the given information

\(\angle KRJ=\angle LRJ = 90^{\circ}\) (given as right angles), \(JK = JL\) (given), and \(JR=JR\) (common side).

Step3: Apply the Hypotenuse - Leg (HL) congruence criterion

In right - angled triangles, if the hypotenuse and one leg are equal, the triangles are congruent. For \(\triangle KJR\) and \(\triangle LJR\), \(JK = JL\) (hypotenuse) and \(JR = JR\) (leg). So, \(\triangle KJR\cong\triangle LJR\) (by HL criterion).

Step4: Use the property of congruent triangles

Since \(\triangle KJR\cong\triangle LJR\), their corresponding parts are equal. So, \(KR = LR\) (corresponding parts of congruent triangles).

Answer:

\(KR = LR\) (because \(\triangle KJR\cong\triangle LJR\) by HL criterion and corresponding parts of congruent triangles are equal)