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As shown in the figure, in RT triangle ABC, angle c = 90 °, angle 1 = equal to angle 2, CD = 1.5, BD = 2.5?
In RT △ DEB, ∠ DEB = 90 °. According to the Pythagorean theorem, de ⊥ EB ⊥ DB ⊥ is 1.5, AC = AE. According to the Pythagorean theorem, de ⊥ EB ⊥ is DB ⊥ i.e. 1.5 ﹣ EB ﹣ 2 = 2.5 ﹣ so EB = 2, a
As shown in the figure, in the RT triangle ABC, ∠ C = 90 ° m is the midpoint of AB, am = an, Mn is parallel to AC Mn = AC
If cm is connected, then cm is the center line on the hypotenuse AB, i.e. am = cm, ∠ cam = ∠ ACM. It can be seen from the drawing that the points n and C are on both sides of the hypotenuse AB, and Mn ‖ AC can be obtained: ∠ cam = ∠ amn
In RT △ ABC, ∠ C = 90 ° the vertical bisector of AB intersects BC at d if ∠ CAD: ∠ DAB = 1:2, find the degree of ∠ B +U
Let ∠ CAD = x, because ∠ CAD: ∠ DAB = 1:2, so ∠ DAB = 2x, and the vertical bisector of AB intersects CB at point D, so if a triangle DAB is an isosceles triangle, then ∠ B = ∠ DAB = 2x,
In the right triangle ABC, because ∠ C = 90 °, so, ∠ B + ∠ cab = 90 °
2X + X + 2x = 90 ° and x = 18 ° respectively, so ∠ B = 2 × 18 = 36 °
As shown in the figure, in △ ABC, ∠ C = 90 ° the vertical bisector of AB intersects BC at D, ∠ CAD: ∠ DBA = 1:2, then the degree of ∠ DBA is______ .
∵ de bisects AB vertically,
∴∠DBA=∠BAD，
∵∠CAD：∠DBA=1：2，
ν if ∠ DBA = 2x, then ∠ bad = 2x, ∠ CAD = x,
∴x+2x+2x=90°，
∴x=18°，
∴∠DBA=2x=2×18°=36°．
As shown in the figure, in △ ABC, ∠ C = 90 ° the vertical bisector of AB intersects BC at D, ∠ CAD: ∠ DBA = 1:2, then the degree of ∠ DBA is______ .
∵ de bisects AB vertically,
∴∠DBA=∠BAD，
∵∠CAD：∠DBA=1：2，
ν if ∠ DBA = 2x, then ∠ bad = 2x, ∠ CAD = x,
∴x+2x+2x=90°，
∴x=18°，
∴∠DBA=2x=2×18°=36°．
As shown in the figure, it is known that in △ ABC, the vertical bisector Mn of ∠ C = 90 ° AB intersects BC at point D. if, ∠ CAD: ∠ DAB = 1:2, calculate the degree of ∠ cab
∵BM=AM DM=DM BD=DA ∠DMB=∠AMD=90°
ν Δ DMB is all equal to △ DMA, ∠ DAB = ∠ CBA
∵∠dab=2∠cad,∠cad+∠dab+∠cab=90°
∴∠cad+2∠cad+2∠cad=90° ====>>5∠cad=90°====>>∠cad=18°
∴∠CAB=3∠CAd=54°
As shown in the figure, in RT △ ABC, ∠ a = 90 ° and the vertical bisector De of BC intersects BC and AC at points D and e respectively, and be intersects with AD at point F. let ∠ C = x, ∠ AFB = y, find the function analytic formula of Y with respect to X, and write the definition domain of function
∵ de bisects BC vertically
be = Ce (1 point)
﹤ EBD = ∠ C = x (1 point)
∵ a = 90 ° and D is the midpoint of BC
/ / ad = DC (1 point)
Ψ DAC = ∠ C = x (1 point)
﹤ ADB = 2x (1 point)
∵ AFB = ∠ EBD + ∠ ADB (1 point)
ν y = 3x (1 point) 0 ° < x < 45 ° (1 point)
As shown in the figure, in RT △ ABC, the vertical bisector De of ∠ ACB = 90 ° intersects AC with E, and the extension of intersection BC is at F. if ∠ f = 30 ° de = 1, then the length of be is______ .
∵∠ACB=90°，FD⊥AB，
∴∠ACB=∠FDB=90°，
∵∠F=30°，
Ψ a = ∠ f = 30 ° (the remainder of the same angle is equal)
The vertical bisector De of AB intersects AC with E,
∴∠EBA=∠A=30°，
In the right angle △ DBE, be = 2DE = 2
So the answer is: 2
As shown in the figure, in RT △ ABC, ∠ ABC = 90 °, the vertical bisector of slope AC intersects point BC and point D, AC crosses point E, and connects be (1) If be is the tangent of the circumscribed circle ⊙ o of ⊙ Dec, calculate the size of ∠ C; (2) When AB = 1, BC = 2, find the radius of △ Dec circumscribed circle
(1) de vertically bisects AC, Dec = 90 °, DC is the diameter of △ Dec circumscribed circle, and the midpoint o of DC is the center of circle; connecting OE, it is also known that be is the tangent line of circle O, EBO + ∠ BOE = 90 °; in RT △ ABC, e is the midpoint of the hypotenuse AC, be = EC, ? EBC = ? OE = OC, ? BOE = 2
As shown in the figure, in RT △ ABC, ∠ ACB = 90 °, BC = 3, AC = 4, the vertical bisector De of AB intersects the extension of BC at point E, then the length of CE is () A. 3 Two B. 7 Six C. 25 Six D. 2
∵∠ACB=90°，BC=3，AC=4，
According to Pythagorean theorem, ab = 5,
The vertical bisector De of AB intersects the extension of BC at point E,
∴∠BDE=90°，∠B=∠B，
∴△ACB∽△EDB，
/ / BC: BD = AB: (BC + CE), and BC = 3, AC = 4, ab = 5,
∴3：2.5=5：（3+CE），
Thus, CE = 7
6．
Therefore, B
RELATED INFORMATIONS
- 1. In the RT triangle ABC, if the angle ACB = 90 degrees, BC = 3, AC = 4, the vertical bisector De of AB intersects the extension of BC at point E, then
- 2. As shown in the figure, in △ ABC, ∠ ACB = 90 °, points D and E are on AB, ad = AC, be = BC. Try to judge whether the size of ∠ DCE is related to the degree of ∠ B. if so, ask for the relationship between them; if not, please determine the degree and explain the reason
- 3. As shown in the figure, in △ ABC, ab = AC, ad ⊥ BC at D, ﹤ bad = 40 °, point E on AC, and AE = ad, calculate the degree of ∠ CDE ditto
- 4. As shown in the figure, ab = AC, ad = AE are known
- 5. It is known that, as shown in the figure, △ ABC is an inscribed regular triangle of ⊙ o, and point P is a moving point on arc BC. This paper explores the relationship between PA, Pb and PC
- 6. The triangle ABC is an equilateral triangle, the triangle ABC is an isosceles triangle, ad = AE, ∠ DAE = 80 °, bad = 15 ° to find the degrees of ∠ CAE and ∠ EDC
- 7. 1. Given △ ABC, we make △ abd and △ ace with AB and AC as the sides, and ad = AB, AC = AE, ∠ DAB = ∠ CAE, and connect DC with be, G and F as DC respectively
- 8. As shown in the figure, in the triangle ABC, ad is the center line on the BC side. The circumference of the triangle abd is 5 smaller than that of the triangle ACD. Can you find the difference between the edge lengths of AC and ab?
- 9. As shown in the figure, we know AB = CD = 1, ∠ ABC = 90 ° and ∠ CBD = 30 ° to find the length of AC
- 10. As shown in the figure, △ ABC, point D is on AC, and ab = ad, ∠ ABC = ∠ C + 30 °, then ∠ CBD=______ Degree
- 11. As shown in the figure, the triangle ABC and the triangle ECD are isosceles right triangles, in which AC = BC, DC = EC, and C on ad, connect AE, de. please find out a pair of congruent triangles in the graph, and write the process of proving their congruence
- 12. It is known that ad is the median line of the triangle ABC, e is the extension of CE at any point on ad, and the intersection of AB and F is proved to be AE / ad = 2AF / BF
- 13. It is known that in △ ABC, ab = AC, BD and CE are the heights on the edge of AC and ab respectively, connecting De Results: (1) △ abd ≌ △ ace; (2) The quadrilateral BCDE is isosceles trapezoid
- 14. As shown in the figure, ad is the height on the hypotenuse of the right angle △ ABC, de ⊥ DF, and de and DF intersect AB, AC and E, f respectively AD＝BE BD．
- 15. As shown in the figure, the chord AB and radius OC of ⊙ o are extended and intersected at point D, BD = OA. If ∠ AOC = 105 °, then ∠ D=______ Degree
- 16. As shown in the figure, the image of the quadratic function y = ax2-4x + C passes through the coordinate origin and intersects with the X axis at point a (- 4,0) (1) Find the analytic formula of quadratic function; (2) If there is a point P on a parabola, s △ AOP = 8, please write out the coordinates of point P directly
- 17. As shown in the figure, △ ABC, ab = AC, points D and E are on the extension line of AB and AC respectively, and BD = CE, de and BC intersect at point F. verification: DF = EF
- 18. As shown in the figure, in △ ABC, ∠ BAC = 90 °, ad ⊥ BC at D, e is a point on AB, AF ⊥ CE is at F, ad intersects CE at G point. It is proved that ∠ B = ∠ CFD
- 19. As shown in the figure, in RT △ ABC, ∠ C = 90 °, BC = AC, points D and E are on BC and AC respectively, and BD = CE, M is the midpoint of AB, and △ MDE is isosceles triangle As shown in the figure, in RT △ ABC, ∠ C = 90 °, BC = AC, points D and E are respectively on BC and AC, and BD = CE, M is the midpoint of AB, and △ MDE is isosceles right triangle. Please explain the reasons
- 20. As shown in the figure, in the triangle ABC, BC = 6, e and F are the midpoint of AB and AC respectively, the moving point P is on the ray EF, BP intersects CE at D, bisector of angle CBP intersects CE at Q, when CQ = 1 / 3 * ce, EP + BP=____ .