C. Perpendicular Planes

26.Show that through a given point A, there can be drawn infinitely many planes perpendicular to a given plane α.

27.In the adjacent figure, DABC is an equilateral triangle and DBDC is an isosceles triangle.

AB = 6 cm and BD = DC = 5 cm are given.

Find AD, if (ABC) ⊥ (BDC).

28.Two planes are perpendicular to each other. Can we draw a line,

a) Perpendicular to both of the planes

b) Parallel to both of the planes

c) Perpendicular to one of the planes and parallel to other plane.

29.In the figure DABC, DBCL and DBKL are equilateral triangles. Given that (ABC) is perpendicular to (BCL) and (BCL) is perpendicular to (BKL).

If AB = 4 cm find AK.

30.In the figure ABCD and CRST are two congruent squares.

Given that AB is perpendicular to BT, BT is perpendicular to TS and BT = TS = 6 cm. Find AS.

31.In the figure DABC is a right triangle and BCLK is a square. Given that AB is perpendicular to BK, AB = 5 cm and BC = cm. Find AK + AL.

32.State the following as true or false.

a. Three planes may be perpendicular to each other.

b. Three lines may be perpendicular to each other.

c. A line may be parallel to both of two intersecting planes.

d. A line may be perpendicular to both of two intersecting planes.

33.State the following as true or false for a space.

a. There are infinitely many planes perpendicular to a line.

b. There are infinitely many lines perpendicular to a line.

c. From a point we can draw only one perpendicular plane to a line.

d. From a point we can draw only one perpendicular line to a line.

e. We can draw infinitely many perpendicular lines to a line.

34.In the figure the planes P and Q are perpendicular to each other and their intersection is the line d.

Given that DABC is an equilateral triangle,

m(<KBC) = 90°,

KC = 20 cm and

AC = 16 cm.

Find AK.

35.In the figure ABCD is a rectangle; DDCT is an isosceles right triangle. Given that,

TC (ABCD)

AD = 8 cm,

AB = 6 cm.

Find AT.

36.In the figure, ABCD and ADEF are rectangles. Given that, ED DC,

AD = 2 cm,

EF = 8 cm.

The semicircle that we draw inside of ABCD is tangent to BC at T. Find FT.

37.In the figure ABCD is a rectangle and CDKL is a square. Given that,

BC CL,

AD = cm and

DK = 5 cm.

Find AL.

D. Distance

38.In the figure E is a plane and P is a point outside of P. We draw aperpendicular line PA to the plane P. Prove that ,

a) If AB = AC then PB = PC.

b) If PB < PC then AB < AC.

39.In the figure AC is perpendicular to plane P. Given that, m( CAE) = 30°,

BE = ED = 5 cm,

AB = AD and

DC = 13 cm.

Find A(DABD).

40.In the figure PH is perpendicular to the plane and PB = 5 cm. Given that H is the center of circumcircle of ABC.

Find PA + PC.

41.An ant is walking 5 m to east then 2 m to south. Then it is climbing on a plane with a 60 inclination for 4 m to the west. What is the distance between the starting point and the end point of the ant.

42.A helicopter is rising for 600 m then going to east for 800 m then to north for 2400 m. What is the distance between the starting and ending point of the helicopter?

43.In the figure line k is parallel to plane P and line t is in P. Distance between k and t is 24 cm. If AR = 7 cm find BR.

44.In a plane there are two parallel lines d and k. A and B are two points on line d and AB = 6 cm. If the distance between these two lines is 5 cm find the area of the triangle ABC where C is a point on line k.

Date: 2015-12-11; view: 1955