![](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, CD is the height of the bottom edge ab of the isosceles triangle ABC. De is parallel to BC and intersects AC at point E. judge whether △ Dec is an isosceles triangle and explain the reason
Delta Dec is an isosceles triangle
Proof: because CD is the height of the base ab of the isosceles triangle ABC,
So D is the midpoint of ab
It's parallel to BC,
Then de = half of BC and E is the midpoint of AC, that is, EC = half of AC
And because AC = BC
So de = EC
So delta Dec is an isosceles triangle
RELATED INFORMATIONS
- 1. (1) As shown in Figure 1, isosceles △ ABC and isosceles △ Dec have a common point C, and ∠ BCA = ∠ ECD, connect be and ad, if BC = AC, EC = DC, prove: be = ad. (2) if △ Dec is rotated around point C to figure 2, figure 3 and figure 4, other conditions remain unchanged, are be and ad still equal? Why?
- 2. In △ ABC, ab = AC, D and E are the midpoint of BC and AC respectively, and △ Dec is an isosceles triangle? RT= =
- 3. In RT triangle ABC, ∠ C = 90 °, ab = 2, radical 2, BC = radical 6, solve this right triangle
- 4. In △ ABC, C-A = π / 2, SINB = 1 / 3, find the value of sina 2. Let AC = √ 6, find the area of △ ABC
- 5. Sina ^ 2 / SINB ^ 2 + cosa ^ 2 * COSC ^ 2 = 1, Tana ^ 2 * cotb ^ 2 = sinc ^ 2 Trigonometric ratio just contact. Seek detailed proof All right, we must add more
- 6. Junior high school triangles are similar to triangles ABC and def. If AB is equal to ab + de and AC is equal to AC + DF, is that ab Triangle similarity in junior high school Triangle ABC and triangle def, if AB than AB + de equals AC than AC + DF, is ab than de equal to AC than DF? Why? If the angle BAC equals the angle EDF, are the two triangles similar? Why?
- 7. If BC = 3, DF = 4, ∠ f = 90 °, then ∠ C =?, s triangle def =?
- 8. In triangle ABC and triangle def, angle a = angle d = 65 degrees, AB / AC = ed / DF, are these two triangles similar? Why?
- 9. If triangle ABC is similar to triangle def, angle a is equal to angle e is equal to 30 degrees, and angle B is equal to 70 degrees, what is angle f equal to?
- 10. In triangle ABC and triangle def, is angle a = angle d = 70 degrees, angle B = 60 degrees, and angle e = 50 degrees similar? Why?
- 11. It is known that in △ ABC, ab = AC, ⊙ o with ab as diameter intersects BC at D and AC at e. it is proved that △ Dec is an isosceles triangle Such as the title
- 12. In the isosceles triangle ABC, ab = AC = 5, then the diameter of the circumcircle of the triangle ABC is________ . I think the problem is similar to the lack of conditions,
- 13. In the isosceles triangle ABC, ab = AC, ad is the middle line on the bottom edge
- 14. Mathematical geometry problem -- in the isosceles triangle ABC, ab = AC, the perpendicular of edge AB intersects with the straight line where AC lies In the isosceles triangle ABC, ab = AC, the acute angle obtained by the intersection of the middle perpendicular of side AB and the line where AC is located is 40 degrees, then the degree of ∠ B is?
- 15. This is a problem of mathematical geometry. How to find the degree of ∠ a in triangle △ ABC AB = AC BC = BD ad = de = EB?
- 16. In RT △ ABC, ∠ C = 90 °, AC = 3, BC = 2, Tana = cotb=
- 17. In △ ABC, if Tana = 2, then Sina =, a, √ 5 / 5, B, 2 √ 5 / 5, C - √ 5 / 5, D-2 √ 5 / 5
- 18. In △ ABC, if B = 5, ∠ B = π 4, Tana = 2, then Sina = 1___ ；a= ___ ．
- 19. In △ ABC, if B = 5, angle B = 45 ° and Tana = 2, then Sina =?, a =?
- 20. As shown in the figure, AP is the height of △ ABC, point DG is on AB and AC respectively, point E F is on BC, quadrilateral defg is rectangular, AP = h, BC = a, let DG = x, the area of rectangular defg is y, try a, h, X to represent Y