Mathematics Triangle Exam Prep
Full explanation, worked examples & memory tricks in the app
🎯 Exam Preparation Kit
Mathematics Triangle Exam Prep
English 10 leveled MCQs Free
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Sample questions with model answers
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7 marks Long answer
In triangle ABC, if AD is the bisector of \(\angle A\) meeting BC at D, then prove that \(\frac{BD}{DC} = \frac{AB}{AC}\).
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Use the Angle Bisector Theorem.
The full exam-length answer is in the app.
7 marks Long answer
ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Show that \(\frac{AE}{ED} = \frac{BF}{FC}\).
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Use properties of similar triangles.
The full exam-length answer is in the app.
7 marks Long answer
A boy of height 1.5 m is walking away from the base of a lamp-post 6 m high at a uniform speed of 2 m/s. Find the length of his shadow after 6 seconds.
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Length of shadow = 4.5 m.
The full exam-length answer is in the app.
7 marks Long answer
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that \(\triangle ABE \sim \triangle CFB\).
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Use the criteria for similarity of triangles.
The full exam-length answer is in the app.
7 marks Long answer
In a \(\triangle PQR\), N is a point on PR such that \(QN \perp PR\). If \(PN \times NR = QN^2\) then prove that \(\angle PQR = 90^\circ\).
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Apply the converse of the Pythagorean theorem.
The full exam-length answer is in the app.
7 marks Long answer
D is a point on the side BC of a triangle ABC such that \(\angle ADC = \angle BAC\) then prove that \(CA^2 = CB \cdot CD\).
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Use the properties of angles and segments in triangles.
The full exam-length answer is in the app.
7 marks Long answer
Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that \(\triangle ABC \sim \triangle PQR\).
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Use the criteria for similarity based on proportional sides.
The full exam-length answer is in the app.
4 marks Medium answer
D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that (i) OBGC is a parallelogram.
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Use properties of midpoints and parallelograms.
The full exam-length answer is in the app.
4 marks Medium answer
D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that (ii) \(EF \parallel BC\).
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Use the properties of parallel lines.
The full exam-length answer is in the app.
4 marks Medium answer
D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that (iii) \(\triangle AEF \sim \triangle ABC\).
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Use the criteria for similarity of triangles.
The full exam-length answer is in the app.
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