Question

<krj and <lrj are right angles
jk = jl
prove: kr = lr
mark everything in the picture first!
what you know\thow you know it
<krj and <lrj are right angles\tgiven
jk = lr\tgiven
\t
△kjr ≅ △ljr
kr = lr

Explanation:

Step1: Identify the common side

In \(\triangle KJR\) and \(\triangle LJR\), \(JR = JR\) (common side in both triangles).

Step2: Apply the Hypotenuse - Leg (HL) congruence criterion

Since \(\angle KRJ\) and \(\angle LRJ\) are right angles (\(\angle KRJ=\angle LRJ = 90^{\circ}\)), \(JK = JL\) (given), and \(JR=JR\) (common side). By the HL (Hypotenuse - Leg) congruence criterion for right - angled triangles, \(\triangle KJR\cong\triangle LJR\).

Step3: Use the property of congruent triangles

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

Answer:

\(KR = LR\)