Lessons 53–54 · 2 lessons · B. Xaydarov, E. Sariqov, A. Qo‘chqorov. Geometry, Grade 9 (textbook for general secondary schools), revised 4th edition. Huquq va Jamiyat Publishing, Tashkent, 2019
54
Test your knowledge
Textbook: pp. 142–144
GoalTest the main knowledge of Chapter IV: projection of a segment, proportional segments, the altitude in a right triangle, chords and secants.
Recall the main rules of the chapter. The projections of segments on parallel lines are proportional to the segments. Parallel lines cutting the sides of an angle make proportional segments. In a right triangle the altitude to the hypotenuse satisfies h² = a_c·b_c, and the legs satisfy a² = c·a_c. In a circle AO·OB = CO·OD and PA² = PB·PC. In a test, before choosing an answer, draw a figure with the given data, choose the matching formula and check the result: for instance, the legs must be shorter than the hypotenuse and the altitude shorter than the legs. If you must find the false statement, check each statement separately.
Worked examples
Projections 8 and 18: h = √144 = 12, c = 26, area = ½·26·12 = 156.
AO = 9, OB = 4, CO = 3: OD = 36/3 = 12. R = 9, p = 15: tangent = √(225 − 81) = 12.
Class activity
“Find the mistake”: a friend solves a problem with a deliberate error (for instance, an altitude longer than a leg); you find the error and explain why.
Practice
1
If the projections are 8 and 18, what is the altitude?
12
2
What is the tangent length to a circle of radius 9 from a point 15 from the centre?
12
3
Parallel lines cut an angle's sides: AB = 6, CD = 9, C₁D₁ = 12. Find A₁B₁.
8
4
Why is the altitude of a right triangle shorter than each leg?
The leg is an oblique and the altitude is a perpendicular; the perpendicular is shorter.