Subjects geometry

Left Triangle 65Feff

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1. Stating the problem: Draw a left triangle, i.e., a right triangle whose right angle is on the left side.\n2. Definition: A right triangle has one angle equal to $90^\circ$.\n3. Properties: The side opposite the right angle is the hypotenuse (the longest side) and the other two sides are the legs.\n4. Orientation: A left triangle is simply a right triangle rotated so the right angle sits at the left vertex A; the geometry and formulas do not change.\n5. Formula: The Pythagorean theorem relates the legs $a,b$ and hypotenuse $c$ by $a^2 + b^2 = c^2$.\n6. Area formula and rule: The area is given by $\frac{1}{2}ab$ where $a$ and $b$ are the legs; remember the legs must meet at the right angle for this formula to apply.\n7. Example setup: Choose legs $a=3$ and $b=4$ as a concrete example to compute the hypotenuse and show steps.\n8. Compute squares: $3^2 = 9$.\n9. Compute squares: $4^2 = 16$.\n10. Sum of squares: $9 + 16 = 25$.\n11. Hypotenuse: $c = \sqrt{25} = 5$.\n12. Explanation in plain language: We picked two perpendicular sides of lengths 3 and 4; by the Pythagorean theorem their opposite side is length 5, so the triangle with the right angle on the left has legs 3 and 4 and hypotenuse 5.\n13. Diagram note: The SVG below shows one clear drawing of a left triangle with vertex A at the left (right angle), B at the top, C at the right; legs AB=b and AC=a, hypotenuse BC=c.\n14. Final answer: The left triangle is a right triangle oriented with the right angle at the left vertex; the drawing gives a visual example.\n
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