In triangle GHJ and triangle KLM, it's given that <G and <K are right angles, segment GH is = to segment KL and <H is = to <L. prove that triangle GHJ is = to triangle KLM/
prove KLM=KNM.give reasons
WHAT IS THE RELATIONSHIP BETWEEN THE PERIMETER OF GHJ AND THE PERIMETER OF KLM?
To prove that triangle GHJ is congruent to triangle KLM, we will use the information given and apply the appropriate congruence criterion.
Given:
1. <G and <K are right angles.
2. Segment GH is equal to segment KL.
3. <H is equal to <L.
To prove GHJ ≅ KLM, we will use the congruence criterion SSS (Side-Side-Side).
Step 1: Show that the corresponding sides are congruent.
- From given information (2), we know that GH = KL.
Step 2: Show that the corresponding angles are congruent.
- From given information (3), we know that ∠H = ∠L.
Step 3: Show that the right angles are congruent.
- Given information (1) states that ∠G and ∠K are right angles. By definition, all right angles are congruent.
By satisfying the SSS congruence criterion and showing that all corresponding sides and angles are congruent, we can conclude that triangle GHJ is congruent to triangle KLM.
To prove that triangle GHJ is equal to triangle KLM, we need to show that their corresponding sides and angles are equal.
Given:
1. <G and <K are right angles.
2. Segment GH is equal to segment KL.
3. <H is equal to <L.
To prove that the triangles are equal, we can use the following steps:
Step 1: Show that segment HJ is equal to segment ML.
Since GH = KL (given) and triangles GHJ and KLM have a right angle at G and K, respectively, we can conclude that HJ = ML using the Pythagorean theorem.
Step 2: Show that <J is equal to <M.
Since <H = <L (given) and the sum of the angles in a triangle is 180 degrees, we have:
<H + <GJH + <J = 180 degrees (angle sum in triangle GHJ)
<L + <KLM + <M = 180 degrees (angle sum in triangle KLM)
Since <G = <K (both are right angles), and <H = <L (given), we can substitute these values:
90 degrees + <GJH + <J = 180 degrees
90 degrees + <KLM + <M = 180 degrees
By subtracting 90 degrees from both equations, we get:
<GJH + <J = 90 degrees
<KLM + <M = 90 degrees
Therefore, we can conclude that <J = <M.
Step 3: Show that <GJH is equal to <KLM.
Since <G = <K (both are right angles) and <J = <M (proven in step 2), we can conclude that <GJH = <KLM.
By showing that all corresponding sides and angles are equal, we have proven that triangle GHJ is equal to triangle KLM.