Statements Reasons
1. GH║KL 1. Given
2. J is the midpoint of HK 2. Given
3. JH ≅ JK 3. Definition of the midpoint of a segment
4. ∠JKL ≅ ∠JHG 4. Alternate interior angles
5. ∠GJH ≅ ∠KJL 5. Vertically opposite angles
6. ΔGHJ ≅ ΔLKJ 6. By ASA theorem of congruence
We have to prove the statement, ∠GHJ = ∠LKJ
Given; GH || KL, J is the midpoint of HK.
To prove; ∠GHJ = ∠LKJ
Given; J is the midpoint of HK,
By definition midpoint of a segment,
The midpoint is the middle part of the line segment J, it is equidistant from both endpoints it is the centroid of the segment of the endpoints.
JH ≅ HK
Then, by the property of alternate interior angles,
∠JKL≅ ∠JKH
Therefore, by the property of vertically opposite angles,
When two lines intersect they form four angles. Vertical angles are the angles that are opposite to each other. Any two intersecting lines form two pairs of vertical angles that are opposite to each other.
∠GJH ≅ KJL
By ASA congruence theorem,
When two triangles are congruent to each other - If two angles and the involved side of one triangle is equivalent to the two angles and the included side of the other triangle.
ΔGHJ ≅ ΔLKJ
Hence Proved.
For more details refer to the link.
https://brainly.com/question/1751208
