![](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>)
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
The vertical bisection is ab
be = AE (2 points)
The circumference of △ ace = AE + EC + AC = be + CE + AC = BC + AC
The circumference of ABC is 24cm, ab = 10cm
∴BC+AC=24-10=14cm
The circumference of ACE is 14 cm
In the triangle ABC, ab = AC, the vertical bisector De of AB intersects BC with E, and the perpendicular foot is d. if the circumference of triangle ABC and AEC are 26 cm and 18 cm respectively, the vertical bisector of AB is 0 Find the length of each side of the triangle ABC
AB + BC + Ca = 26 cm AE + EC + Ca = 18 because AE + EC = be + EC = BC, so BC + AC = 18, ab = 8 cm, because AB = AC, so AC = 8 cm, so BC = 10 cm, so triangle
As shown in the figure, in △ ABC, if the vertical bisector of AC intersects AC at e and BC at D, the circumference of △ abd is 12cm, AC = 5cm, then AB + BD + ad=______ cm；AB+BD+DC=______ Cm; the circumference of △ ABC is______ cm．
∵ De is the vertical bisector of line AC,
∴AD=CD，
∴AD+BD=CD+BD，
The circumference of abd is 12 cm,
∴AB+BD+AD=12cm，AB+BD+DC=12cm，
∵AC=5cm，
The circumference of △ ABC = (AB + BD + DC) + AC = 12 + 5 = 17cm
So the answer is: 12, 12, 17
As shown in the figure, the circumference of △ ABC is 19cm, the vertical bisector De of AC intersects BC at D, e is perpendicular foot, AE = 3cm, then the circumference of △ abd is______ cm．
∵ the vertical bisector De of AC intersects BC with D, and E is the perpendicular foot
∴AD=DC，AC=2AE=6cm，
The circumference of ABC is 19 cm,
∴AB+BC=13cm
The circumference of △ abd = AB + BD + ad = AB + BD + CD = AB + BC = 13cm
Therefore, fill in 13
In △ ABC, ab = AC, the vertical bisector Mn of AB intersects AC at point D and ab at point E. if AE = 6 and the circumference of △ CBD is 20, calculate the circumference of △ ABC
∵ Mn vertical bisection ab
∴AD=BD
AE=BE=1/2AB=6,AB=12
∵ △ CBD perimeter = BC + BD + CD = BC + CD + ad = BC + AC = 20
∴△ABC=AB+BC+AC=12+20=32
In △ ABC, De is the vertical bisector of AC, AE = 5cm, and the circumference of △ CBD is 24cm. Calculate the circumference of △ ABC
In ABC, De is the vertical bisector of AC,
∴AD=CD，CE=AE=5cm，
∴AC=AE+CE=10cm，
The circumference of CBD is 24cm,
∴BC+CD+BD=BC+AD+BD=BC+AB=24（cm），
The circumference of △ ABC is: AC + AB + BC = 10 + 24 = 34 (CM)
As shown in the figure, in △ ABC, De is the vertical bisector of AC, AE = 5cm, the circumference of △ ABC is 25cm, and calculate the circumference of △ abd
The circumference of △ ABC = AB + AC + BC
=AB+2AE+BD+DC=25
De bisects AC vertically, so ad = DC
The circumference of △ abd = AB + BD + ad
=AB+BC=25-AC=25-10=15Cm
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．
∵ de bisects BC vertically,
∴DB=DC．
∵AC+AD+DC=14cm，
∴AC+AD+BD=14cm，
AC + AB = 14cm
And ∵ AB-AC = 2cm,
Let AB = xcm, AC = YCM
According to the meaning of the title, we get
x+y＝14
x−y＝2 ，
The solution
x＝8
y＝6
The length of AB is 8cm and that of AC is 6cm
As shown in the figure, in △ ABC, ab = 5cm, AC = 3cm, and the vertical bisector of BC intersects AB, BC at D and e respectively, then the circumference of △ ACD is______ cm．
∵ De is the vertical bisector of BC,
∴CD=BD，
The circumference of △ ACD = AC + CD + ad = AC + AD + BD = AC + AB,
AC = 3cm, ab = 5cm,
The circumference of △ ACD is 3 + 5 = 8cm
So the answer is: 8
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
As shown in the figure: AF ⊥ BD at point F, de ⊥ BC at point e through point D,
∵ a = 120 ° in trapezoidal ABCD,
∴∠ABC=60°，∠ADB=∠DBC，
∵ BD bisection ∵ ABC,
∴∠ABD=∠DBC=30°，
∴∠ABD=∠ADB=30°，
∴AB=AD，
∵BD=BC=4
3，
∴BF=2
3，
∴AB=AD=BF
cos30°=4，
De = 1
2BD=2
3，
Therefore, s trapezoid ABCD = 1
2（AD+BC）×DE=1
2×（4+4
3）×2
3=4
3+12．
Therefore, D
RELATED INFORMATIONS
- 1. 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
- 2. In △ ABC, ab = 4 3，AC=2 3, ad is the center line of BC side, and ∠ bad = 30 °, then BC=______ .
- 3. 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?
- 4. 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
- 5. 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
- 6. It is known that the circumference of an isosceles triangle is 10cm, the waist length is xcm, and the base length is YCM. ① take the waist length x as the independent variable, write out the functional relationship between Y and X, and find the value range of the independent variable x; ② when y = 3, find the value of X;
- 7. Given that the circumference of an isosceles triangle is 20cm, the functional relationship between waist length y (CM) and base x (CM) is
- 8. In the isosceles triangle ABC, given Sina: SINB = 1:2 and base BC = 10, then the circumference of △ ABC is______ .
- 9. If the two sides a, B of an isosceles triangle satisfy | 2a-3b + 5 | + (2a + 3b-13) 2 = 0, then the circumference of the isosceles triangle is______ .
- 10. The circumference of an isosceles triangle is 18, one side is 5, and the other two sides are______ .
- 11. 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．
- 12. 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．
- 13. 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,
- 14. 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
- 15. 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
- 16. 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______ .
- 17. In isosceles △ ABC, ab = AC = 13cm, BC = 10cm. Find the radius of the circumcircle of isosceles △ ABC
- 18. Are two right triangles with an angle of 60 ° congruent? Are two isosceles triangles congruent with an obtuse angle
- 19. The method of drawing auxiliary line in the proof of congruent triangle
- 20. 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