Circle L has segment LJ and segment LK as radii. Those 2 segments are perpendicular. Segment KM and segment JM are tangent to circle L. Is triangle JLM congruent to triangle KLM? Please explain.
<KLJ is right given
<LKM = <LJM is right (tangent to circle perpendicular to radius)
MJ || KL and KM || LJ congruent interior and exterior angles (all right angles)
the remaining angle in the square is right and all sides are equal .
therefore LM is diagonal of square
diagonal cuts || lines so opp interior angles JML=KLM =JLM=KML
angles the same and hypotenuse the same and radii the same, side angle side
TriangleJLM, Triangle KLM
JM=KM as Length of tangents to a circle from external point is equal
Also LJ=LK as they are radii of circle
LM is common side!
Hence by SSS congruency principle the 2 triangles are congruent =)
To determine if triangles JLM and KLM are congruent, we need to check if their corresponding sides and angles are congruent. Let's analyze each part:
1. Corresponding sides:
- We have segment LJ and segment LK as radii of the circle. Since these two radii have the same length, we can conclude that LJ is congruent to LK.
- We also have segment KM and segment JM as the tangents to circle L. Tangents drawn from the same external point to a circle are of equal length, so KM is congruent to JM.
2. Corresponding angles:
- We know that segment LJ and segment LK are perpendicular radii. Perpendicular lines form right angles. Thus, angle JLM and angle KLM are both right angles and are congruent.
Based on the above analysis, all corresponding sides and angles of triangles JLM and KLM are congruent. Therefore, we can conclude that triangle JLM is congruent to triangle KLM.