Justifying steps in geometry
Types of exercises: justifying a step of the reasoning, drawing a conclusion about a figure.
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Choose the conclusion that the given facts justify
In trapezium ABCD with bases AB and CD, the base AB is 3 times as long as the base CD. The diagonals AC and BD meet at the point S. Which conclusion is true?
Choose the theorem that justifies this step of the reasoning
The lines RB and CF are parallel, and the segments RF and BC meet at the point S. Why is |∠RSB| = |∠FSC|?
Choose the conclusion that the given facts justify
The points A, B, C and D lie on a circle, and C and D lie on the same side of the line AB. We know that |∠ACB| = 55°. Which conclusion is true?
Choose the theorem that justifies this step of the reasoning
The points C, M, B and E lie on a circle, and B and E lie on the same side of the line CM. We know that |∠CBM| = 63°. Why is |∠CEM| = 63°?
Choose the conclusion that the given facts justify
The point D lies on the side AC and the point E on the side BC of triangle ABC, with DE ∥ AB and |CD| : |DA| = 1 : 4. Which conclusion is true?
Choose the theorem that justifies this step of the reasoning
The lines KB and LM are parallel, and the segments KM and BL meet at the point S. Why is |∠BKS| = |∠LMS|?
Choose the conclusion that the given facts justify
The segment AB is a diameter of a circle, and the point C lies on the circle, with |AC| = 9 cm and |BC| = 12 cm. Which conclusion is true?
Choose the theorem that justifies this step of the reasoning
The points C, D, P and A lie on a circle, and P and A lie on the same side of the line CD. We know that |∠CPD| = 50°. Why is |∠CAD| = 50°?
Choose the conclusion that the given facts justify
The lines PA and PB are tangent to a circle with centre O at the points A and B. We know that |∠APB| = 80°. Which conclusion is true?
Choose the theorem that justifies this step of the reasoning
The lines BM and NP are parallel, and the segments BP and MN meet at the point S. Why is |∠MBS| = |∠NPS|?
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