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In trapezoidal ABCD, AD / / BC, ab = DC, angle ABC = 80 °, e is the point on lumbar CD, connecting be, AC and AE, if angle ACB = 60 ° and angle EBC = 50 ° Find the degree of the triangle EAC
Connecting BD with AC and EF, BCF and ADF are all regular triangles,
It can be proved that CB = CE. E, F and B are on the circle with C as the center and CE as the radius, thus the angle EFD = EDF = 40 ° can be proved
Because EF = ed, it is easy to prove triangle ade congruent AFE
So angle CAE = angle DAE = 1 / 2 angle DAC = 30 degree
RELATED INFORMATIONS
- 1. As shown in the figure, in the known square ABCD, e is the point on ad, BF bisects ∠ EBC intersects DC at point F
- 2. It is known that in square ABCD, point E is the point above ad, BF bisects ∠ EBC, intersects DC at point F, and the proof is: be = AE + CF
- 3. Geometry e is a point of ad on the edge of square ABCD, BF bisects ∠ EBC intersects DC with F, and proves that EB = AE + CF
- 4. Trapezoid ABCD AB parallel DC ad = BC AE, BF are the height of two waist respectively, and AE, BF intersect with point o Let BAE = x and C = y find out and prove the relation between X and y
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- 6. It is known that in rectangular ABCD, ab = 2CB, point E is on DC, and AE = AB, then ∠ EBC=___ .
- 7. As shown in the figure, in rectangular ABCD, e is a point on DC, AE = AB, ab = 2ad, then the degree of ∠ EBC is______ ．
- 8. Given AB = 2BC of rectangle ABCD, take point E on CD so that AE = EB, then what is the angle EBC equal to
- 9. Given AB = 2BC of rectangle ABCD, take point E on CD to make AE = EB, then the angle EBC is equal to A 60 B 45 C 30 D 15
- 10. E is a point on the edge CD of rectangle ABCD, and AE = AB, ab = 2BC, find the degree of ∠ EBC
- 11. For the isosceles trapezoid ABCD, ad is parallel to BC, ad = 2cm, BC = 8cm, e is the midpoint of the lumbar CD, be divides the trapezoid into two parts, the perimeter difference is 3cm, and calculates the length of ab I only have the second grade of junior high school, and I am learning the median line of triangle and trapezoid. I hope you can help me solve the problem according to the direction of this theorem
- 12. It is known that e is the midpoint of the waist BC of the trapezoidal ABCD, and ab + CD = ad
- 13. As shown in the figure, in rectangular ABCD, AF ⊥ BD, perpendicular foot is f, ∠ DAF = 3 ∠ BAF, calculate the degree of ∠ fac
- 14. As shown in the figure, in square ABCD, ∠ AFD = 65 ° AF and BD intersect at E
- 15. As shown in the figure, in square ABCD, ∠ DAF = 25 °, AF intersects diagonal BD at e, intersects CD at F, then ∠ bec=______ Degree
- 16. As shown in the figure, in square ABCD, ∠ DAF = 25 °, AF intersects diagonal BD at e, intersects CD at F, then ∠ bec=______ Degree
- 17. As shown in the figure, e and F are two points on the diagonal AC and BD of rectangle ABCD, and AE = DF. Prove the congruent triangle COF of triangle BOE
- 18. As shown in the figure, e and F are two points on the diagonal BD of the quadrilateral ABCD, AE ‖ CF, AE = CF, be = DF
- 19. As shown in the figure, e and F are two points on the diagonal BD of the quadrilateral ABCD, AE ‖ CF, AE = CF, be = DF
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