Geometry Math Problems Urgent and detailed process 20 points in 10 minutes

Obviously, there are two more hours and minutes at 6 o'clock, and the angle between the hour and minute hands is 110 degrees, before 6:30 and after 6:30.

If you go out at 6 o'clock x, you should go out before 6:30 o'clock.

180 degrees - (x 60) * 360 + (360 12) * (x 60) = 110 degrees.

x=140/11

Set 6:00 a.m. to go home, and it should be after 6:30.

y-30) 60]*360-(360 12)*(y60)=110 degrees.

y=580 11, so he goes out y-x=440 11=40 minutes.

2: (1) Because M is the midpoint of AC, AC=8cm, therefore, MC=4cm, similarly, N is the midpoint of BC, CB=6cm, so CN=3cm

So mn=7cm

2) Yes. Because m is the midpoint of ac, mc=(1 2)ac. Similarly, n is the midpoint of BC, cn=(1 2)CB.

So mn=mc+cn=(1 2)ac+(1 2)cb=(1 2)(ac+cb)=(1 2)a

3) m is the midpoint of ac, so mc = (1 2)ac. Similarly, n is the midpoint of BC, cn=(1 2)CB.

Because C is on the extension line of AB, MN = (1 2) * (AC-CB) = (1 2) B

1 question. Because.

The quadrilateral ABCD is a parallelogram of the quadrangle pattern.

So. ab//cd

Because. E and F are the points on the DC and BA extension sails.

So. af//de

So. f+∠fce=180°

Because. f=∠e

So. e+∠fce=180°

So. The quadrilateral AFCE is a parallelogram.

So. af=ce

2. The letters in your question do not match the diagram.

If you think about it carefully, the problem is very simple, you pass the point p to make the vertical line of the side AC, which is called AC at the point E, because the angle EAP = 30 degrees, so PE=1 2AP, that is, BP+1 2AP=BP+PE, the minimum value is the shortest BE, that is, the height of the edge AC=(3*A) 2.

You can draw a picture, it will be very clear, I hope it helps you!

Just kidding, point p and point d coincide The minimum value A 2 ap is exactly bisected Bac Bap = 30° In a right triangle, the right angle of 30 degrees is half the hypotenuse.

Both sides can be squared at the same time.

As known, s pab=s pcd, ab=cd;

then the heights of the two triangles are equal;

That is, the distance from point P to OA and OB is equal;

According to the angular bisector theorem, we get: po bisects aod.

Point F and point E are not marked, so let's ...... here】

Over P as PE vertical AB PF vertical CD

S-triangle pab=s-triangle PCD

1/2ab*pe=1/2cd*pf

ab=cdpe=pf

PO bisects the angle AOD

Make a perpendicular line on ab,cd through the point p, the perpendicular foot is, e,f, because the area of the triangle pab and the triangle pcd are equal, so they are congruent, so, pb=pc, pbe pce, the perpendicular foot 2 ninety degrees are equal, so pbe= pcf, so these 2 triangles are congruent, so pe=pf so op bisects aod

The set a= solution a=

and because b is contained in a

So b= or b= or b= or b= or b= empty set.

1) When b=, i.e. x=-2

a²-2a-8=0

A=(2) When b=, i.e., x=4

a²+4a+4=0

A=-2(3) When b=, i.e., x1=-2, x2=4a, (1) and (2) need to be satisfied.

Get a=-2

4) When b = empty set.

A -4 (a -12) = 48-3a 0 to get a 4 or a -4

In summary, the set of values of the real number a is (negative infinity, -4) 4, positive infinity).

Because a= is a=

and because b is contained in a

i.e. b= or b= or b=

When b=. x=-2.

4-2a+a 2-12=0 gets a=

When b=. x=4 gives a 2+4a+4=0 gives a=-2 when b=x1=-2 and x2=4 gives a=-2

x -2x-8 gives x=4 or x=-2, bringing the two values into x squared + ax + —12 = 0

Solve two equations.

a +4a+4=0 or a -2a-8=0

then a=[-2,4].

Complementary Angles Definition of Complementary Angles: If the sum of two angles is a flat angle, then the two angles are called complementary angles, and one of the angles is called the complementary angle of the other angle.

A + C = 180°, A = 180°- C, C Complement Angle = 180° - C i.e.: A Complement Angle = 180° - A

The nature of the co-angle:

The complementary angles of the same angle are equal. For example: a+ b=180°, a+ c=180°, then: c= b.

The complementary angles of equal angles are equal. For example: a+ b=180°, d+ c=180°, a= d, then: c= b.

Co-angle If the sum of two angles is a right angle, then these two angles are called co-angles with each other, referred to as co-angles, and it can also be said that one of the angles is the co-angle of the other angle. A + C = 90°, A = 90°- C , C co-angle = 90° - C i.e.: A co-angle = 90° - A

The nature of the co-angle:

The co-angles of the same angle are equal. For example: a+ b=90°, a+ c=90°, then: c= b.

The co-angles of equal angles are equal. For example: a+ b=90°, d+ c=90°, a= d, then: c= b.

The co-angle of 20° is (70°) and the complementary angle is (160°).

The co-angle of 17° is (73°), and the complementary angle is (163°).

The co-angle of 70°32 minutes is (19°28 minutes), and the complementary angle is (109°28 minutes).

The co-angle of 32°51 minutes and 18 seconds is (57°8 minutes and 42 seconds), and the complementary angle is (147°8 minutes and 42 seconds).

Conclusion: The co-angle of the angle is 90 ° different from the complementary angle of the angle

Solution: (1) When p is tangent to ab in motion, let the tangent point be m, connect pm, then amp=90°, apm abc, ,ap=t, ab= ,

2) Proof of: BC AC, PD AC, BC DP, when , ap=, PC=4-, ec=

be=bc-ec=3- ,adp abc, ,pd= ,pd=be, when t= the quadrilateral pdbe is a parallelogram (9 points).