It is proved that the height on the base of an isosceles triangle with a vertex angle of 120 degrees is equal to half of the waist length May have to discuss the classification, a good solution to give more points

It is proved that the height on the base of an isosceles triangle with a vertex angle of 120 degrees is equal to half of the waist length May have to discuss the classification, a good solution to give more points

In the triangle ABC, ab = AC, angle BAC = 120 degrees
When ad is perpendicular to D, the angle BAC is bisected
So: angle bad = 60 degrees
Angle B = 30 degrees
So: ad = AB / 2
The height at the bottom is half the length of the waist

If the top angle of an isosceles triangle is 120 degrees and the height on the bottom edge is 1 cm, how many centimeters is its waist length and how many square centimeters is its area I'll give you a free answer today

According to the theorem of three lines in an isosceles triangle, the high line is the bisector of an angle. Therefore, the line divides the triangle into two congruent right triangles with an angle of 60 degrees. In these two right triangles, the opposite side of the 30 ° angle is 1 cm high, so the hypotenuse, that is, the waist is 2 cm, and the half of the bottom edge is the root 3 cm. Therefore, the bottom edge is 2 pieces of 3 cm, and the area is the root 3 cm 2

As shown in the figure, if the vertex angle of the isosceles triangle ABC is 120 ° and the waist length is 10, then the height ad on the bottom edge is=______ .

As shown in the figure,
∴∠B=1
2（180°-120°）=30°．
∴AD=1
2Ab = 5
The height of the bottom edge ad = 5

If the waist length of an isosceles triangle is 5 and the length of its bottom edge is 6, then the height on its bottom edge is () A. 5 B. 3 C. 4 D. 7

Known, ab = AC = 5, BC = 6, ad ⊥ BC, find the length of AD
∵AB=AC=5，AD⊥BC，BC=6，
∴BD=CD=3，
∴AD=
AC2−CD2=
25−9=4．
Therefore, C

As shown in the figure, if the vertex angle of the isosceles triangle ABC is 120 ° and the waist length is 10, then the height ad on the bottom edge is=______ .

As shown in the figure,
∴∠B=1
2（180°-120°）=30°．
∴AD=1
2Ab = 5
The height of the bottom edge ad = 5

If the height of the base edge of an isosceles triangle is equal to half of the waist length, then the base angle of the isosceles triangle is equal to______ Degree

∵AD⊥BC，
∴∠ADB=90°，
∵AD=1
2AB，
∴∠B=30°，
∵AB=AC，
∴∠C=∠B=30°，
So the answer is: 30

If the height of the base edge of an isosceles triangle is equal to half of the waist length, then the top angle of the isosceles triangle is equal to______ Degree

∵ in the right angle △ abd, ad = 1
2AB，
∴∠B=30°，
∵AB=AC，
∴∠C=30°，
∴∠BAC=120°．

In the isosceles triangle ABC, the vertex angle a is 36 degrees and BD is the bisector of angle ABC. What is the value of AD than AC

BD is the bisector of angle ABC, AB / BC = ad / CD
In the isosceles triangle ABC, if the vertex angle a is 36 degrees and BD is the bisector of angle ABC, then there is ad = BD = BC, ab = AC, CD = AC ad
AC / ad = ad / (AC AD)
That is, ad 2 + ad * AC-AC 2 = 0
Because of AD
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In the isosceles triangle ABC, the vertex angle

Ad = BD = BC (deduced from angle),
If ad = 1, CD = x, then because the triangle BCD is similar to ABC, AD / AC = BD / AC = AC / BC,
=>1/（1+X）=X/1,=>X=(√5-1)/2,
=>AD/AC=2/(√5+1)

As shown in the figure, it is known that in isosceles △ ABC, the vertex angle ∠ a = 36 ° and BD is the bisector of ∠ ABC The value of AC is equal to () A. 1 Two B. 5−1 Two C. 1 D. 5+1 Two

∵ isosceles ᙽ ABC, vertex angle ∠ a = 36 °
∴∠ABC=72°
And ∵ BD is the angular bisector of ∵ ABC
∴∠ABD=∠DBC=36°=∠A
And ∵ C = ∵ C
∴△ABC∽△BDC
∴CD
BC＝BC
AB
Let ad = x, ab = y,
∵∠A=∠ABD，∴BD=AD，
Then BC = BD = ad = x, CD = y-x
∴y−x
x＝x
y. Suppose X
If y = k, then the above equation can be changed to 1
k-1=k
The solution is: K=
5−1
2, then ad
The value of AC is equal to
5−1
2．
Therefore, B