Questions and Answers
What can be inferred about triangle PQR where angle Q is a right angle and PM is perpendicular to QR?
In triangle ABD where angle A is a right angle and AC is perpendicular to BD, which equation is correct?
What is true for triangle ABC if it is isosceles and ABC is also a right triangle?
For an equilateral triangle ABC with each side measuring 20 units, what is the length of each side?
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What is a property of the diagonals in a quadrilateral?
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Study Notes
Right Triangle Properties
- Triangle PQR is a right triangle with angle Q as the right angle.
- Point M is located on side QR such that PM is perpendicular to QR.
- To demonstrate: PM² = QM × MR.
Relationships in Right Triangle ABD
- Triangle ABD is also a right triangle with angle A as the right angle.
- AC is perpendicular to BD, leading to several key relationships:
- Prove that AB² = BC × BD.
- Prove that AC² = BC × DC.
- Prove that AD² = BD × CD.
Isosceles Triangle Characteristics
- Triangle ABC is isosceles, with two sides equal.
- It is also noted that triangle ABC is a right triangle.
Equilateral Triangle Properties
- In an equilateral triangle ABC, each side measures 20 units.
- This ensures all angles are equal, specifically 60 degrees.
Diagonal Properties of a Quadrilateral
- It is to be proven that the diagonals of a quadrilateral have specific properties, potentially highlighting relationships between angles and sides.
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Description
Prove various properties of triangles including right-angled triangles, isosceles triangles, and equilateral triangles. Solve problems involving altitudes, perpendicular bisectors, and diagonals.
