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In △ ABC, ab = AC, ∠ BAC = 80 ° and P is a point in △ ABC, so that the angle PBC = 10 ° and ∠ PCA = 20 °. Find the degree of ∠ PAC
Take a point d below BC, so that the triangle abd is an equilateral triangle, connecting DP and DC, so ad = AB = AC ∠ DAC = ∠ BAC - ∠ bad = 20, so ∠ ACD = ∠ ADC = 80, because AB = AC, ∠ BAC = 80, so ∠ ABC = ∠ ACB = 50, so ∠ CDB = 10 = ∠ BPC, and ∠ DCB = 30 = ∠ PCB, BC = CB, so △ BDC ≌ △ BPC P
The difference between the positive and the oblique two methods of Surveying and drawing
The length of X direction is constant, the length of Y direction is constant, and the length of Y direction becomes 1 / 2
What are the advantages and disadvantages of the two methods? When to use the two methods
It is easier to see the shape of the geometry directly than the oblique two survey drawing method
The positive isometric drawing method is more suitable for drawing plane graphics, while the oblique two isometric drawing method is more suitable for drawing space three-dimensional graphics
How to understand oblique dichotomy
The method of drawing direct view chart is called oblique two survey drawing
1. Take x-axis and y-axis which are perpendicular to each other in the known graph, and draw them as corresponding x-axis and y-axis when drawing the visual graph. The two axes intersect at O-axis, so that the angle of x-axis and y-axis is 45 degrees, and the plane they determine represents the horizontal plane
2. Given the line segments parallel to X axis or Y axis in the graph, draw the line segments parallel to X axis or Y axis in the visual graph
3. The length of the line segment parallel to the x-axis in the given graph remains unchanged in the visual graph; the length of the line segment parallel to the y-axis is half of the original length
The popular point is:
The coordinate system should be established properly,
The longitudinal axis inclines 45 degrees;
Copy parallel to the horizontal axis,
Take half parallel to the longitudinal axis
The drawing method of high one oblique two survey
On the horizontal plane a, there is a right triangle with B as the right angle, and the BC side is parallel to the horizontal plane. Use the oblique two side drawing method to make (AC = 5, ab = 4, BC = 3)
1、 The AC side is parallel to the Y axis
2、 The AB side is parallel to the Y axis
This problem requires that in the rectangular coordinate system.
The rules of oblique dichotomy are as follows
(1) Take the mutually perpendicular axes ox and oy from the known figures. When drawing a visual graph, draw it as the corresponding axis o'x ', o'y', so that ∠ x'o'y '= 45 ° (or 135 °)
(2) Given the line segments parallel to X axis or Y axis in the graph, draw them parallel to X 'axis or y' axis in the visual graph.
(3) The length of the line parallel to the x-axis in the given graph remains unchanged in the visual graph, and the length of the line parallel to the y-axis is half of the original.
1 set AC on the Y axis
2 set AB on the Y axis
Using the rules, just find B
() is called axisymmetric figure
(in a plane, if a figure is folded along a straight line, the parts on both sides of the line can completely coincide) it is called an axisymmetric figure
What are the functions of axisymmetric figures in life
What are the functions of axisymmetric graphics in life? There are three!
1. For the sake of beauty, for example, the architecture of Tian'anmen Square is symmetrical and beautiful;
2. Keep balance, such as the wings of an airplane;
3. Special work needs, such as pentagram, paper cutting
If the area and shape of the figures on both sides of the line are equal, then the figure must be axisymmetric
No, it should be a straight line through a figure. If the figures on both sides of the line are completely coincident and the shapes are equal, then the figure must be axisymmetric
Why can a circle be closed
Circle can not be closed, there will be a diamond gap in the middle, unless filled with other graphics
A Pentagon is an axisymmetric figure, which can also be densely laid______ ．
A regular pentagon is an axisymmetric figure. Each inner angle of a regular pentagon is 180 ° - 360 °
RELATED INFORMATIONS
- 1. As shown in the figure, in △ ABC, ab = AC, ∠ BAC = 80 °, point P is within △ ABC, ∠ PBC = 10 °, PCB = 30 °, calculate the degree of ∠ BAP What are you doing?
- 2. If the inscribed circle of RT triangle is tangent to the hypotenuse AB at D, and ad = 1, BD = 2, then s ABC =? AB is the hypotenuse If the inscribed circle of RT triangle and hypotenuse AB are tangent to D, and ad = 1, BD = 2, then s ABC =? AB is hypotenuse How to use area
- 3. In △ ABC, the vertical bisectors of AB and AC intersect BC at points E and f respectively. If ∠ BAC = 115 °, then ∠ EAF=______ Degree
- 4. In △ ABC, ∠ C = 90 ° and the intersection line BC of AB is at D. if ∠ bad - ∠ DAC = 22.5 °, then the degree of ∠ B is______ ．
- 5. It is known that in △ ABC, points D, e and F are points on BC, AB and AC respectively, AF is parallel to ED, and AF = ed, extend FD to point G, so that DG = FD, and verify that ED and Ag are equally divided,
- 6. (1 / 3) the known triangles ABC, (|) BD and CE are bisectors of angle B and angle c, respectively. Through point a, make AF vertical BD, Ag vertical CE, the perpendicular feet are f, G, connecting FG (1 / 3) the known triangles ABC, (|) BD and CE are bisectors of angle B and angle c, respectively. Through point a, make AF vertical BD, Ag vertical CE, and the perpendicular feet are f, G, connecting FG. (2) if C
- 7. In ABC, BD is the inner bisector of angle B, CE is the outer bisector of angle c, AF is perpendicular to BD, Ag is perpendicular to CE, FG and ABC?
- 8. As shown in the figure, BD is the extension of the intersection of the middle line AE ⊥ BD on the edge AC of △ ABC at the point ECF ⊥ BD. be + BF. = 2bd is proved at the point F It's sloppy
- 9. As shown in the figure, in △ ABC, BD and CD divide ∠ ABC and ∠ ACB equally, and try to explain ∠ d = 90 ° + & # 189; ∠ a
- 10. In the triangle ABC, BD.CD They are the diplomatic bisector of angle ABC and angle ACB
- 11. As shown in the figure, we know that the side length of equilateral triangle ABC is 3, M is a point on AC, passing through point m, make me parallel AB, intersect BC at point E, make MF ⊥ AB at point F, let AF = x, the median line length of trapezoidal emfb is y, find out the function analytic formula of Y and X, and write out the value range of X
- 12. AB = ad ∠ ABC = ∠ ADC, AC and BD intersect at point O. it is proved that AC is the vertical bisector of BD
- 13. Each vertex of the triangle ABC makes a parallel line AD / / be / / FC, which intersects with the extension of BC, Ca and BA at points D, e and f respectively Prove s triangle def = s double triangle ABC
- 14. As shown in the figure, △ ABC is an equilateral triangle, the bisectors of ∠ ABC and ∠ ACB intersect at O, Bo and Co, and the vertical bisectors of CO intersect at e and F As shown in the figure, △ ABC is an equilateral triangle, the bisectors of ∠ ABC and ∠ ACB intersect at points o, Bo and Co, the vertical bisectors of BC intersect at points E and F, and the perpendicular feet are m and N respectively
- 15. In the quadrilateral ABCD, point O is the midpoint of CD, Ao and Bo bisect ∠ DAB, ∠ ABC, ∠ AOB = 120 ° respectively, and prove AD + Half DC + BC = ab
- 16. Is a axisymmetric figure
- 17. Draw two circles to make the figure have two symmetrical axes
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- 19. List one or two phenomena that contain scientific truth in daily life
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