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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
∵ De is the vertical bisector of ab,
∴AD=BD，
The circumference of △ BDC is BC + CD + BD = BC + CD + ad = BC + AC,
∵BC=6，AC=8，
The circumference of △ BDC is 6 + 8 = 14
In the isosceles triangle ABC, the vertical bisector of one waist AB intersects the other waist AC at g. if AB = 10 and the circumference of △ GBC is 17, then the base BC is () A. 5 B. 7 C. 10 D. 9
Let the midpoint of AB be d,
∵ DG is the vertical bisector of ab
ν GA = GB (the distance from one point on the vertical bisector to the two ends of the line segment is equal),
The circumference of triangle GBC = GB + BC + GC = GA + GC + BC = AC + BC = 17,
And ∵ the triangle ABC is an isosceles triangle, and ab = AC,
∴AB+BC=17，
∴BC=17-AB=17-10=7．
Therefore, B
As shown in the figure, BD is the bisector of the base angle of the isosceles △ ABC. If the base angle ∠ ABC = 72 ° and the waist AB length is 4cm, then the bottom BC length is______ cm．
∵ BD is the bisector of the base angle of ᙽ ABC, if ᙽ ABC = 72 °, a = 36 °, C = 72 °, abd = CBD = 36 °, BDC = 72 °, BD = BC = ad, let BC = x, then ad = BD = x, DC = 4-x, ∵ BCD ∵ ABC,
If the circumference of the isosceles △ ABC is 16 and the height on the base BC is 4, then the area of △ ABC is______ .
Let the base length be 2x
The waist length is 16 − 2x
2=8-x．
Using Pythagorean theorem: (8-x) 2 = x2 + 42,
∴x=3，
The area of △ ABC is 1
2×6×4＝12．
So the answer is: 12
If the circumference of the isosceles △ ABC is 16 and the height on the base BC is 4, then the area of △ ABC is______ .
Let the base length be 2x
The waist length is 16 − 2x
2=8-x．
Using Pythagorean theorem: (8-x) 2 = x2 + 42,
∴x=3，
The area of △ ABC is 1
2×6×4＝12．
So the answer is: 12
If the circumference of the isosceles △ ABC is 16 and the height on the base BC is 4, then the area of △ ABC is______ .
Let the base length be 2x
The waist length is 16 − 2x
2=8-x．
Using Pythagorean theorem: (8-x) 2 = x2 + 42,
∴x=3，
The area of △ ABC is 1
2×6×4＝12．
So the answer is: 12
The base edge BC of the isosceles triangle ABC is 10 and its circumference is 36. The area of () of triangle ABC So how to find the height of the triangle ABC? Who said clearly will give who points!
Waist length = (36-10) × 2 = 13
The height of the triangle = √ (13? - 5?) = 12
Area of triangle = 10 × 12 △ 2 = 60
The waist length of the isosceles triangle ABC is 5 / 6 of the base, and the area of the triangle ABC is 108
Let the bottom edge length a
The waist length of the isosceles triangle ABC is 5 / 6 of the base
The height ad on the bottom edge of ABC = √ [(5 / 6A) 2 - (1 / 2a) 2] = 2 / 3A
∴½×2/3a×a=108
a²=324
∵a＞0
∴a=18
The height ad on the bottom edge of the triangle ABC = 18 × 2 / 3 = 12
As shown in the figure, ⊙ o takes one waist ab of the isosceles ⊙ ABC as its diameter, which intersects the other waist AC to e and BC to d Verification: BC = 2DE
Proof: connect ad,
∵ AB is the diameter of ⊙ o,
∴∠ADB=90°，
And ∵ AB = AC,
Ψ B = ∠ C, BD = DC, that is BC = 2dc,
∵ quadrilateral ABDE is a quadrilateral inscribed in a circle,
∴∠CED=∠B，
And ∠ B = ∠ C,
∴∠CED=∠C，
∴DE=DC，
∴BC=2DE．
As shown in the figure, it is known that the base edge BC of the isosceles triangle ABC is 20, D is a point on waist AB, and CD = 16, BD = 12? Look at the analysis carefully and do it again
Let AB = x, ad = x-12ac = x, CD = 16 △ ADC, in which x = (X-12) 2 + 16? X = 50 / 3, perimeter = 50 / 3 × 2 + 20 = 160 / 3 (2) ad
RELATED INFORMATIONS
- 1. 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
- 2. 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;
- 3. Given that the circumference of an isosceles triangle is 20cm, the functional relationship between waist length y (CM) and base x (CM) is
- 4. In the isosceles triangle ABC, given Sina: SINB = 1:2 and base BC = 10, then the circumference of △ ABC is______ .
- 5. 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______ .
- 6. The circumference of an isosceles triangle is 18, one side is 5, and the other two sides are______ .
- 7. It is known that the circumference of an isosceles triangle is 24cm. The center line on a waist divides the triangle into two. The difference of the circumference between the two triangles is 3cm. To find the length of each side of an isosceles triangle, the procedure is as follows @I'm not his uncle
- 8. Given the center line on the waist of an isosceles triangle, divide the circumference of the triangle into 9 cm and 15 cm, and calculate the length of each side of the triangle
- 9. The circumference of isosceles triangle is 20cm. Write the functional relationship between the base length YCM and waist length xcm (x is the independent variable) (2) write the value range of the independent variable
- 10. Given that the circumference of an isosceles triangle is 20cm and the waist length is xcm, then the value range of waist length x of this isosceles triangle is -- (x is an integer)
- 11. 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?
- 12. In △ ABC, ab = 4 3，AC=2 3, ad is the center line of BC side, and ∠ bad = 30 °, then BC=______ .
- 13. 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
- 14. 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
- 15. 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．
- 16. 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．
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- 18. 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
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