![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
In the triangle ABC, ab = AC, the center line be of triangle ABC divides the circumference of triangle into two parts of 9cm and 12cm, and calculates the length of BC in triangle ABC You have to draw your own pictures, The length of the center line is also included in the perimeter of the two parts
If the triangle AB + AE = 9, then CE + BC = 12, because AE = EC, ab = AC, therefore: 2Ab + BC = 12 + 9 = 21bc-ab = 12-9 = 3 can be obtained from above: 3bC = 27BC = 9. Similarly, if AE + AB = 12, EC + BC = 9, 2Ab
In the triangle ABC, ab = AC, CD is the height on the bottom edge, the circumference of triangle ABC is 16cm, and the circumference of triangle ACD is 12cm. Find the length of AD
AB = AC, ad is the height on the bottom edge, BD = CD
The circumference of triangle ABC is 16cm, that is ab + AC + BC = 16, that is 2Ac + 2CD = 16, AC + CD = 8
The circumference of triangle ACD is 12cm, AC + CD + ad = 12, ad = 12-8 = 4
As shown in the figure, we know that the base edge of the isosceles triangle ABC is BC = 20cm, D is a point on waist AB, and CD = 16cm, BD = 12cm. Find the circumference of △ ABC
∵ BC = 20cm, CD = 16cm, BD = 12cm ᙽ BC BC BC BC BC ? BC ? BC ? AB = AC ? AC = AD + BD = AD + 12 ? AC ? AC ? ad ? ad ? ad ? ad ? ad ? ad ? BC
Known isosceles triangle ABC, ab = AC, BC = 20cm, D is a point on AB, and CD = 16cm, BD = 12cm
Solution: let ad be X
Because DB = 12 BC = 20 CD = 16
And this is a group of Pythagorean numbers
So the triangle DBC is a right triangle
The square of AC = the square of X + the square of 16
So (x + 12) 2 = x2 + 16 squared
X=14/3
AB+AC+BC=160/3
Given the isosceles triangle ABC, base BC = 20, D is a point on AB, and CD = 16, BD = 12, find the length of AD
In △ BCD, △ BCD is a right triangle from 122 + 162 = 202. Let ad = x, then AC = 12 + X,
According to Pythagorean theorem, x 2 + 162 = (x + 12) 2 and x = 14 are obtained
3．
∴AD=14
3．
Given that the median line of the waist length of an isosceles triangle divides its circumference into two parts of 15cm and 12cm, the base length of this isosceles triangle is___ .
∵ the circumference of an isosceles triangle is 15cm + 12cm = 27cm. If the waist length and bottom edge length of the isosceles triangle are xcm and YCM respectively, we can get x + 12x = 1512x + y = 12 or x + 12x = 1212x + y = 15 (4 points), x = 10Y = 7 or x = 8y = 11 (3 points)
As shown in the figure, in the isosceles triangle ABC, AC = AB = 12cm, the vertical bisector of AB intersects AC at point D, and the circumference of △ BCD is 21cm, what is the length of bottom BC
∵ the vertical bisector of AB intersects AC at point D
∴AD=BD
The circumference of △ BCD
=BD+BC+CD
=AD+CD+BC
=AC+BC
∵AC+BC=21
AC=12
∴BC=21-12=9
It is known that in the isosceles triangle ABC, ab = AC and the circumference is 16 cm. The median line BD on the edge of AC divides △ ABC into two triangles with perimeter difference of 4cm Find the length of each side of the triangle ABC
In this triangle, let AB = 2x, ad = AC = x, BC = y
4X+Y=16
2X-Y=4
These two triangles are actually the difference between AB and BC. BD is the common line
Hope to adopt
It is known that the circumference of the isosceles triangle ABC is 16cm, ad is the bisector of the vertex angle, AB ratio ad = 5:4, and the circumference of △ abd is 12cm
Ad is the top bisector and the triangle is isosceles triangle
Ad is perpendicular to BC and BD = BC
AB / ad = 5:4
That is cos ∠ bad = 4 / 5
Sin∠BAD=3/5
AB:BC=5:6
2AB+BC=16
AB=AC=5
BC=6
As shown in the figure, the circumference of the isosceles △ ABC is 50cm, ad is the height on the bottom edge, and the circumference of △ abd is 40cm, then the length of ad is______ cm．
∵ ad is the height on the bottom edge,
∴BD=CD，
The circumference of ABC is 50cm,
∴AB+BD=1
2×50=25cm，
The circumference of abd is 40 cm,
∴AD=40-25=15cm．
So the answer is: 15
RELATED INFORMATIONS
- 1. Given that the circumference of the isosceles triangle ABC is 40cm, ad is the height on the bottom edge, and the circumference of the triangle abd is 30cm, what is the length of ad
- 2. As shown in the figure, in the isosceles triangle ABC, ab = AC, point D is a point on BC, de ∥ AC intersects AB at point E, DF ∥ AB intersects AC at point F, ① As shown in Figure 1, when point D is on BC, there is de + DF = AB, please explain the reason. ② as shown in Figure 2, when point D is on the extension line of BC, please refer to figure 1 to draw the correct figure, write down the relationship between De, DF and AB, and write the proof process,
- 3. It is known that Mn is the vertical bisector of line AB, and C and D are two points on Mn (1) Δ ABC, △ abd are isosceles triangles; （2）∠CAD=∠CBD．
- 4. As shown in the figure, given that AB is 2cm longer than AC, the vertical bisector of BC intersects AB at D, crosses BC at e, and the circumference of △ ACD is 14cm, then ab=______ cm，AC=______ cm．
- 5. As shown in the figure: the circumference of △ ABC is 24cm, ab = 10cm, the vertical bisector De of edge AB intersects BC, the edge is at point E, and the perpendicular foot is D, calculate the circumference of △ AEC
- 6. As shown in the figure, it is known that in trapezoidal ABCD, BD bisection ∠ ABC, ∠ a = 120 ° and BD = BC = 4 3, then s trapezoid ABCD = () A. 4 Three B. 12 C. 4 3-12 D. 4 3+12
- 7. In △ ABC, ab = 4 3，AC=2 3, ad is the center line of BC side, and ∠ bad = 30 °, then BC=______ .
- 8. In the isosceles triangle ABC, the vertical bisector of one waist AB intersects the other waist AC at g. given AB = 10, the circumference of triangle GBC is 17, then the length of bottom BC is?
- 9. As shown in the figure, given that the vertical bisector of the sides of the isosceles triangle ABC and ab intersects AC at point D and ab at e, ab = AC = 8, BC = 6, calculate the circumference of △ BDC
- 10. Given that circle O passes through the three vertices of triangle ABC, ab = AC, the distance between the center of circle O and BC is 3, and the radius of circle is 7, find the length of ab
- 11. If the circumference of the isosceles △ ABC is 10 cm, the bottom edge length is y cm, and the waist length is x cm, then the value range of waist length x is______ .
- 12. In isosceles △ ABC, ab = AC = 13cm, BC = 10cm. Find the radius of the circumcircle of isosceles △ ABC
- 13. Are two right triangles with an angle of 60 ° congruent? Are two isosceles triangles congruent with an obtuse angle
- 14. The method of drawing auxiliary line in the proof of congruent triangle
- 15. Can I divide two triangles with 24 ', 84' and 104 ', 52' angles into two isosceles triangles with a straight line (if yes, please write down the divided? B If you can, write the top angle readings of the two isosceles triangles
- 16. The area and perimeter of an congruent triangle are equal. Are the two triangles with the same area and perimeter congruent triangles?
- 17. The isosceles triangle ABC with base BC is still isosceles triangle after being divided into two smaller triangles by a line passing through a vertex Draw all the situations and mark the angles
- 18. In the triangle ABC, ab = AC, the line passing through a vertex intersects the opposite side of D. the line divides the original triangle into two isosceles triangles In the triangle ABC, ab = AC, the line passing through a vertex intersects the opposite side of D. the line divides the original triangle into two isosceles triangles. Find the degree of the three inner angles of the triangle ABC.
- 19. The degree of the top angle of an isosceles triangle is four times that of the base angle. How many degrees are the base angle and the top angle of the isosceles triangle? What triangle is this?
- 20. If an interior angle of an isosceles triangle is 80 degrees, how many degrees or degrees does the top angle differ from the base angle?