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In △ ABC, if the degree ratio of angle a, angle B and angle c is 2:3:5, then what triangle is △ ABC
right triangle
They are 90 degrees, 36 degrees and 54 degrees respectively
Let the side lengths of the inner angles a, B and C in △ ABC be a, B and C respectively, and the angle a = 60 degrees and C = 3B. Find the value (2) CoSb of (1) a / b
Let the side lengths of the inner angles a, B and C in △ ABC be a, B and C respectively, and the angle a = 60 degrees and C = 3B. Find the value (2) Co of (1) a / b
In the triangle ABC, a, B and C are the opposite sides of the inner angles a, B and C respectively, and 2A Sina = (2B + C)
In triangle ABC, a, B and C are opposite sides of inner angles a, B and C respectively, and 2asina = (2B + C) SINB + (2C + b) sinc
1. Find the size of A,
2. If SINB + sinc = 1, try to judge the shape of triangle ABC,
Analysis: ∵ Sina / a = SINB / b = sinc / C = 1 / 2R ∵ 2A ^ 2 = (2B + C) B + (2C + b) C = 2B ^ 2 + 2C ^ 2 + 2BC ∵ B ^ 2 + C ^ 2-A ^ 2 = - BC, that is, cosa = (b ^ 2 + C ^ 2-A ^ 2) / 2BC = - 1 / 2A = 120 °, B + C = 60 ° SINB + sinc = SINB + sin (60-b) = SINB + √ 3 / 2 * cosb-1 / 2 * SINB = √ 3 / 2 * CoSb + 1 / 2 * S
In △ ABC, D, e, f are on BC, CA, AB respectively, and de ‖ AB, DF ‖ AC. the proof is AE / AC + AF / AB = 1
Idea: using the proportional relationship under parallel lines, prove: because of DF / / AC, so: BF / BA = BD / BC (1) because of De / / AB, so: BD / BC = AE / AC (2) (1), (2) two simultaneous: BF / AB = AE / AC (3) to (3) left end Transformation: BF / AB = (ab-af) / AB (4) simultaneous (3), (4) get: AE / AC = (ab-af) / AB = 1 -
As shown in the figure, given that point C is a point on △ ABC side BC, ∠ B = ∠ C, de ⊥ AB is at point E, DF ⊥ AC is at point F, when point D is at what position, de = DF? Explain the reason
Angle a bisector
If de = DF, then ∠ AED = 90 °= ∠ AFD, ad = ad, we can know △ AED ≌ △ AFD
Therefore, ead = fad
Conversely, if ∠ ead = ∠ fad, then △ AED ≌ △ AFD can be obtained, so de = DF
To prove that the sum of internal angles of a quadrilateral is 360 degrees
Divide a quadrilateral into two triangles because
Sum of internal angles of triangle = 180 degree
therefore
Sum of internal angles of quadrilateral = sum of internal angles of 2 triangles = 2 × 180 ° = 360 °
Who has many ways to prove the sum of internal angles of quadrilateral?
Get a picture
Method 1: divide into two triangles, then the sum of internal angles is 180 * 2 = 360 degrees
Method 2: find any point O inside the quadrilateral, divide it into four triangles, and then subtract the perimeter angle from point o
&Nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 180 * 4-360 = 360 degrees
Method 3: find a point o on any side of a quadrilateral, divide it into three triangles, and then subtract the flat angle led by point o
&Nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 180 * 3-180 = 360 degrees
Method 4: find any point o on the outside of the quadrilateral, divide it into three triangles, and then subtract the sum of the internal angles of △ AOD
&Nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 180 * 3-180 = 360 degrees
Prove the interior angle of irregular quadrilateral and 360 degrees?
11 ways to speed up
Diagonally open, two triangles, the inner angle of the triangle and 180 degrees, two on 360 degrees
A polygon is also divided into several triangles by finding a point. Therefore, the sum of the inner angles of the polygon is (n-2) * 180 degrees
It's in the book
Why is the sum of the internal angles of a quadrilateral 360 degrees?
By connecting a diagonal line, the sum of internal angles of quadrilateral = sum of internal angles of two triangles = 2 * 180 = 360
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