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In the isosceles triangle ABC, when AB = AC rotates △ ABC clockwise about point B for 35 degrees, point a just falls on point D on BC, and point C falls on point E, then ∠ Dec=
According to the meaning of the title, ∠ Abe = 35 °, △ ABC ≌ △ DBE, △ DBE is also isosceles triangle
∴∠DBE=∠DEB=35°
∵△ABC≌△DBE
∴BC=BE
∴∠BEC=∠BCE=(180°-∠CBE)/2 = (180°-35°)/2=72.5°
∴∠DEC=∠BEC-∠BED =72.5-35° = 37.5°
In the RT triangle ABC, angle c = 90 °, BC = 10, s triangle ABC = 50 times root 3 / 3, solve this right triangle
S△ABC=(1/2)AC*BC=5AC=50/√3,
AC=10√3/3,
tanA=BC/AC=√3,
∠A=60°,∠B=30°,
AB=2AC=20√3/3.
If Sina = 2 * SINB, Tana = 3tanb, then cosa =?
tana=3tanb
So:
sina/cosa=3sinb/cosb
Because Sina = 2sinb
So:
2sinb/cosa=3sinb/cosb
So: cosa = (2 / 3) * CoSb
Is that what you want?
In △ ABC, a = 5, B = 3, then the value of sina / SINB is
Sina / SINB = A / b = 5 / 3 (sine theorem)
In △ ABC, the opposite sides of ﹥ a. ﹥ B. ﹥ C are A.B.C, and a: B: C = 3:4:5, so the value of sina + SINB can be obtained
It is known that △ ABC is a right triangle,
And Sina = 3 / 5
sinB=4/5
So Sina + SINB = 7 / 5
In triangle ABC and triangle def, is angle a = angle d = 70 degrees, angle B = 60 degrees, and angle e = 50 degrees similar? Why
Similarly, according to the internal angle and 180 degrees of the triangle, the three angles of the two triangles are equal
180-70-60=50
180-70-50=60
As shown in the figure, connect the midpoint D, e, F of each side of triangle ABC, and try to prove that triangle DEF is similar to triangle ABC
Angle DAE = angle BAC, Ce: de = 3:4 verification: (1) angle ABC similar angle ade (2) angle ADB similar angle AEC
Certification:
Because D, e and F are the midpoint of AB, BC and Ca respectively
The median lines of △ ABC are de, EF and DF
∴DE/AC=EF/AB=DF/BC=1/2
{△ def ∽ ABC (three sides corresponding to two triangles in proportion are similar)
In △ ABC and △ def, it is known that ∠ a = 35 °, B = 60 °, e = 35 ° and F = 60 ° are not identical,
Say reason, add a what condition can get two triangle congruence
Is it necessary to add an ab = EF to be congruent
I want to ask if the vertex angle in the triangle can not be corresponding, but in congruent triangle, the vertex angle must be corresponding
Two triangles are similar in themselves, and if any of their sides are equal, they are congruent
In addition, it's better to match the top angle to form a good habit, so that you can write out what side and angle are equal,
In the following three conditions, the congruence of ABC and def cannot be determined
If ad is to be congruent, the angles between the two sides must be equal, or the common sides of the two corners must be equal, or the three sides must be equal. The equality of the sides of a and D is not the corresponding side of the two corners
If the following conditions are met, it can be judged that △ ABC and △ def are congruent
A.AB=DE,∠B=∠E,AC=DF
B.AB=DF,∠A=∠D,AC=DE
C.BC=EF,∠B=∠E,AB=DF
D.AB=DE,∠A=∠F,BC=EF
B
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