Score to pass: 70%
Related MCQS
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2. End of Unit Test on Inverse and Composite Transformations in 2D for S3 Students
3. End of Unit Test on Enlargement and Similarity in 2D for S3 Students
4. End of Unit Test on Collinear Points and Orthogonal Vectors for S3 Students
5. End of Unit Test on Percentage Interest and Proportion for S3 Students
6. End of Unit Test on Linear and Quadratic Functions for S3 Students
7. End of Unit Test on Quadratic Equations for S3 Students
8. End of Unit Test on Simultaneous Equations and Inequalities for S3 Students
9. End of Unit Test on Algebraic Fractions for S3 Students
10. End of Unit Test on Number Bases for S3 Students
11. End of Unit Test on Problems on Sets for S3 Students
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Right-Angled Triangles Unit Summary
1. Pythagoras theorem
Consider the right-angled triangle ABC shown in figure below:
Figure 1
Pythagoras theorem states that: \(a^{2}+b^{2}=c^{2}\)
2. The median theorem of a right angled triangle states that. The median from the right-angled vertex to the hypotenuse is half the length of the hypotenuse.
Consider the right angled triangle XYZ
Figure 2
\(WX=\frac{1}{2}YZ\), hence, WX=WZ=WY.
3. The altitude theorem of a right angled triangle states that: “The altitude to the hypotenuse of a right-angled triangle is the mean proportional between the segments into which it divides the hypotenuse.”
Consider the right-angled triangle EFG.
Figure 3
\(\frac{\text{ altitude }}{\text{ part of hypotenuse }}=\frac{\text{ other part of hypotenuse }}{\text{ altitude }}\)
\(\frac{HG}{EH}=\frac{HF}{HG}\)
4. The leg theorem of a right-angled triangle states that “the leg of a right-angled triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.” It can be simply presented as;
\(\frac{\text{ leg }}{\text{ hypotenuse }}=\frac{\text{ projection of leg }}{\text{ leg}}\)
From Figure 3, we can write: \(\frac{EG}{EF}=\frac{EH}{EG}\) or \(\frac{GF}{EF}=\frac{HF}{GH}\)
5. Trigonometric ratios
Consider the Figure 4 below:
Figure 4
\(\sin \theta =\frac{BC}{AC}\), \(\cos \theta =\frac{AB}{AC}\), \(\tan \theta =\frac{BC}{AB}\).
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