Proving Right-Angled Triangles with Pythagoras' Theorem
In a geometrical problem involving intersecting lines on the x-axis, we demonstrate the formation of right-angled triangles by applying Pythagoras' theorem. Through visual aids and mathematical explanations, the concept of right angles within triangles is illustrated with clarity and precision.
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Presentation Transcript
Crossed Lines Don Steward
Crossed Lines Two lines: 2? + 4 = ? and ? + 2? = 8 meet on the x-axis. Show, by using Pythagoras' theorem, that the triangle formed by the lines and the ? ???? is right-angled.
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 2? = 4 2? + 2 = ? ? + 2? = 6 2? + 3 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 2? = 10 ? + 2? = 8 2? + 4 = ? 2? + 5 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 3? = 6 3? + 2 = ? ? + 3? = 9 3? + 3 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 3? = 12 ? + 3? = 15 3? + 4 = ? 3? + 5 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 4? = 12 ? + 4? = 8 4? + 2 = ? 4? + 3 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 4? = 16 ? + 4? = 20 4? + 4 = ? 4? + 5 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 5? = 10 ? + 5? = 15 5? + 2 = ? 5? + 3 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
Crossed Lines Crossed Lines Show, by using Pythagoras' theorem, that Show, by using Pythagoras' theorem, that the triangle formed by the lines and the the triangle formed by the lines and the ? ???? is right-angled. ? ???? is right-angled. ? + 5? = 20 ? + 5? = 25 5? + 4 = ? 5? + 5 = ? meet on the x-axis. meet on the x-axis. Two lines: Two lines: SIC_25 SIC_25 and and
