In a convex quadrilateral ABCD, Da = DB = DC = BC, then the degree of the largest angle in the quadrilateral is () A. 120°B. 135°C. 150°D. 165°
Solution: let ∠ CDA = x, ∠ ABC = y, ∵ Da = DB = DC = BC, ∵ BDC = ∠ DBC = ∠ DCB = 60 °, ∵ DBA = ∠ DAB, ∵ DAC = ∠ DCA, ∵ DBA + ∠ bad + ∠ BDA = 180 °,
RELATED INFORMATIONS
- 1. In RT △ ACB, ∠ ACB = 90 °, AC = 3, BC = 4, the moving circle O passing through point C is tangent to the hypotenuse AB at the moving point P, and the value range and maximum value of CP are obtained
- 2. In △ ABC, ∠ C = 90 °, AC = 4cm, BC = 5cm, point D is on BC, and CD = 3cm. There are two moving points P and Q starting from point a and point B at the same time, where point P moves along AC to terminal C at the speed of 1cm / s, and point Q moves along BC to terminal C at the speed of 1.25cm/s. Passing point P, PE ‖ BC is connected to point E, and EQ is connected (1) The length of AE and De is expressed by the algebraic expression containing x; (2) when the point Q moves on BD (excluding points B and D), let the area of △ EDQ be y (cm2), find the functional relationship between Y and time x, and write out the value range of the independent variable x; (3) when the value of X is, the △ EDQ is a right angle triangle
- 3. As shown in the figure, given that point E is on the edge ab of △ ABC, point D is on the extension line of Ca, and point F is on the extension line of BC, what is the size relationship between ∠ ACF and ∠ D? Please give reasons
- 4. As shown in the figure, given that point E is on the edge ab of △ ABC, point D is on the extension line of Ca, and point F is on the extension line of BC, what is the size relationship between ∠ ACF and ∠ D? Please give reasons
- 5. As shown in the figure, the triangle ABC is an equilateral triangle, and D is the midpoint on the side ab. it is known that the area of the triangle BDE is 5 square centimeters. Find the area of the equilateral triangle ABC
- 6. In △ ABC, ab = AC, be = CF, EF intersect BC with D
- 7. As shown in the figure, it is known that ad, be and CF are respectively the heights of the three sides of △ ABC, h is the perpendicular, and the extension line of ad intersects the circumscribed circle of △ ABC at point G
- 8. As shown in the figure, in the quadrilateral ABCD, ∠ bad = ∠ ABC, ad = BC, AC intersects with point o at BD. let's say that the triangle OAB is an isosceles triangle
- 9. As shown in Figure 1, in △ ABC, points e.d.f ab.bc.ca If ad bisects ∠ BAC, then the quadrilateral AEDF is a diamond?
- 10. In the triangle ABC, ab = BC, the point D E F is the midpoint on the side of BC AC AB respectively
- 11. As shown in the figure, in △ ABC, ab = AC, ∠ BAC = 108 °, D is on AC and BC = AB + CD, the proof is: BD bisects ∠ ABC
- 12. As shown in the figure, in the isosceles trapezoid ABCD, it is known that ad ∥ BC, ab = CD, AE ⊥ BC are in E, ∠ B = 60 °, DAC = 45 ° and AC = 6?
- 13. As shown in the figure, in RT △ ABC, ∠ C = 90 °, am is the middle line on the side of BC, sin ∠ cam = 35, then the value of tanb is () A. 32B. 23C. 56D. 43
- 14. In rectangular ABCD, AE is perpendicular to BD, and the angle DAE = 2 angle BAE?
- 15. Ad is the height of triangle ABC, be is the midline angle on the side of AC, CBE = 30 degrees to prove ad = be
- 16. As shown in Figure 7-11, in the known triangle ABC, ad is perpendicular to D, BC is equal to D, AE is equal to ∠ BAC (2), if ∠ B > C, try to explain ∠ DAE = 1 / 2 (∠ B - ∠ C)
- 17. It is known that in the oblique triangle ABC, the straight line with high BD and CE intersects at h, and the angle a = 45 degrees, so the degree of the angle BHC can be calculated? No picture, if you can,
- 18. In known quadrilateral ABCD, angle abd = 12 °, angle DBC = 36 °, angle ACB = 48 ° and angle ACD = 24 °, try to find the degree of angle ADB I can draw pictures according to the title,
- 19. As shown in the figure, in △ ABC, be bisects ∠ ABC intersects AC at point E, de ‖ BC intersects AB at point D, ∠ ade = 70 ° and calculates the degree of ∠ DEB Don't use the formula (one outer angle of a triangle is equal to the sum of two nonadjacent outer angles),
- 20. In the triangle ABC, ab = 15, AC = 20, the height ad on the side of BC = 12, try to find the length of BC? I give bonus points to the detailed process, get 7 within the 25 do not talk about I want the process of 7