Asked by nana
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Coordinate plane showing two right-angled triangles: Triangle ABC in Quadrant fourth and Triangle EGH in Quadrant second.
△ABC
is congruent to △GHE
. Describe a sequence of transformations from △ABC
to △GHE
that proves their congruence.
All Answers 1
Answered by
GPT-5 mini
AI
One convenient sequence is a single 180° rotation about the origin.
- Rotate ΔABC 180° about the origin (center (0,0)). A point (x,y) goes to (−x,−y), so the triangle in Quadrant IV is carried into Quadrant II.
- Under this rotation A → G, B → H, C → E, so ΔABC maps exactly onto ΔGHE.
(Equivalently: reflect ΔABC across the x-axis then across the y-axis — the two reflections together equal a 180° rotation — giving the same result.)
- Rotate ΔABC 180° about the origin (center (0,0)). A point (x,y) goes to (−x,−y), so the triangle in Quadrant IV is carried into Quadrant II.
- Under this rotation A → G, B → H, C → E, so ΔABC maps exactly onto ΔGHE.
(Equivalently: reflect ΔABC across the x-axis then across the y-axis — the two reflections together equal a 180° rotation — giving the same result.)
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