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In △ ABC, ∠ ACB = 100 °, AC = BC, point D is on AB, and BD = BC, point E is on AC, and AE = ad, EF ⊥ DC is on f 1. Find the degree of ∠ def 2: If AC = BC is removed from the title, what about the degree of ∠ def 3: If the body weight ∠ ACB = 100 ° is changed to ∠ ACB ＞∠ a, other things remain unchanged, what is the relationship between ∠ def and ∠ ACB
It is very important to draw a picture according to the title. 2. The number of the angles of the two bases of the isosceles triangle is equal. The title gives the top angle 3. The sum of the angles a and B of the triangle is 1804. The sum of the angles a and B of the two isosceles triangles is 360 def = (360-80) / 2-90
It is known that in △ ABC, ∠ BAC = 90 °, ad ⊥ BC at point D, be bisection ∠ ABC, intersection ad at point m, an bisection ∠ DAC, intersection BC at point n Verification: the quadrilateral amne is rhombic
It is proved that: ∵ ad ⊥ BC, BDA = 90 °, ∵∵ BAC = 90 °, ABC + ∠ C = 90 °, ABC + ∠ bad = 90 °, ∵ bad = ∠ C, ? an bisection ? DAC, ? can = ∠ Dan, ? ban = ∠ bad + ∠ Dan, ? be ⊥ an
As shown in the figure, in △ 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 with D, and the bisector of CBP intersects CE with Q, when CQ = 1 At 3ce, EP + BP=______ .
As shown in the figure, the extended BQ cross ray EF is at m, ∵ E and F are the midpoint of AB and AC respectively, ? EF ∥ BC, M = ∵ CBM, ? BQ is the bisector of ? CBP, ? PBM = ∠ PBM, ? BP = PM, ? EP + BP = EP + PM = em, ∵ CQ = 13ce, EQ = 2cq
As shown in the figure, in △ ABC, BC = 6, e, f are the midpoint of AB and AC respectively, point P is on ray EF, BP intersects CE with D, point q is on CE and BQ bisects ∠ CBP, let BP = y, PE = X. when CQ = 1 At 2ce, the functional relationship between Y and X is______ When CQ = 1 When nce (n is a constant not less than 2), the functional relationship between Y and X is______ .
The extended BQ is the bisector of CBP, and BQ is the bisector of CBP, ? BQ is the bisector of ? CBP, ? BQ is the bisector of ? CBP, ? PBK, ? EKB = \\57575757575757578780 575757575757575757575757575757575757575757575757575757? BQ is the bisection of constant)
As shown in the figure, in △ ABC with uncertain shape and size, BC = 6, e and F are the midpoint of AB and AC respectively, P is on the extension line of EF or EF, BP intersects CE on D, q is on CE, and BQ bisects ∠ CBP. Let BP = y, PE = X (1) When x = 1 When 3ef, calculate the value of s △ DPE: s △ DBC; (2) When CQ = 1 When 2ce, find the function relation between Y and X; (3) When CQ = 1 When 3ce, find the function relation between Y and X; When CQ = 1 When nce (n is a constant no less than 2), the function relation between Y and X is written directly
(1) ∵ E and F are the midpoint of AB and AC respectively, x = 13ef, EF ∥ BC, and EF = 12bc, EDP ? CDB, ᙽ epbc = 16, s △ DPE: s △ DBC = 1:36; (2) extend BQ to meet EF at K, ∵ EK ∥ BC, ? EKB = ∠ KBC, and ? BQ is the bisector of ? PBK = ? EK
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
It is proved that DG ∥ AE is made through point D and passed to point BC at point G, as shown in the figure,
∴∠1=∠2，∠4=∠3，
∵AB=AC，
∴∠B=∠2，
∴∠B=∠1，
∴DB=DG，
And BD = CE,
∴DG=CE，
In △ DFG and △ EFC
∠4＝∠3
∠DFG＝∠EFC
DG＝CE ，
∴△DFG≌△EFC，
∴DF=EF．
In the triangle ABC, BC is greater than AC, point D is on BC, DC = AC, bisector CF of angle ACB intersects ad at F Point E is the midpoint of AB, connecting EF 1. Verify EF parallel BC 2. If the area of the quadrilateral BDFE is 6, calculate the area of the triangle abd
(1)
∵ AC = CD, CF bisection ∵ ACB
The point F is the midpoint of AD (three lines in one)
∵ point E is the midpoint of ab
ν EF ‖ BC (median line)
(2）
∵EF‖BC
∴△AEF∽△ABD
∴S△AEF：S△ABD=（AE：AD）^2=1/4
ν s quadrilateral BDFE: s △ abd = 3 / 4
The area of △ abd = 8
In the triangle ABC, BC > AC, point D is on BC, DC = BC, bisector CF of angle ACB intersects ad at F, e is the midpoint of AB and connects EF It is proved that EF paralleled BC. 2 the area of quadrilateral bdef is 6. Find the area of triangle ABC
The title is wrong. D is on BC. How can DC = BC? Go and draw a picture for me
In the triangle ABC, BC is greater than AC, point D is on BC, DC = AC, bisector CF of angle ACB intersects ad at point F, point E is the midpoint of AB, connecting EF If the area of the triangle abd is 6, find the area of the quadrilateral bdef
In △ CFD and △ CFA, DC = AC, CF = CF, ∠ ACF = ∠ DCF -- △ CFD is all equal to △ CFA ＂ AF = FD, e is the midpoint of ab - ＂ AEF is similar to △ abd - ＂ s △ AEF: s △ abd = (AE: ab) ^ 2 - ＂ s △ AEF = s △ abd / 4 = 3 / 2 ＂ s quadrilateral bdef = s △ abd-s △ AEF = 6-3 / 2
In the triangle ABC, BC is greater than AC, point D is on BC, DC = AC, bisector CF of angle ACB intersects ad with F, point E is the midpoint of AB, connecting EF In the triangle ABC, BC is greater than AC, point D is on BC, DC = AC, bisector CF of angle ACB intersects ad with F, point E is the midpoint of AB, connecting EF. If the face of quadrilateral BDFE is 6, calculate the area of triangle abd
ACD of triangle is isosceles triangle, f is the midpoint of AD, EF is the median line of abd of triangle, EF is parallel to BD, triangle AEF is similar to triangle ADB
Thus, the area of triangle abd is 8
RELATED INFORMATIONS
- 1. In the triangle ABC, the angle ACB = 90 degrees, ad bisects the angle BAC, De is perpendicular to e, EF intersects AC to F, and EC intersects ad to o
- 2. As shown in the figure, △ ABC is an isosceles triangle, ∠ ACB = 90 ° and the midpoint D of BC is de ⊥ AB, and the perpendicular foot is e to connect CE. Find the value of sina ∠ ace
- 3. In the triangle ABC, the bisector of angle B and the bisector of angle c intersect at point DDG / BC, and acab is proved to be GF = bg-cf at two points of FG
- 4. As shown in the figure: in isosceles RT △ ABC, ∠ C = 90 degrees, AC = 8, f is the midpoint of AB edge, points D and e move on AC and BC sides respectively, and keep ad = CE, connect We need the whole proof process. Thank you
- 5. [function] point P is an image of inverse scale function and positive scale function y = - 2x. PQ is perpendicular to X axis, and the coordinate of perpendicular foot is (2,0) If point m is on the inverse scale function image and the area of △ MPQ is 6, find the coordinates of point M Missing two words Point P is the intersection of an image with an inverse scale function and a positive scale function y = - 2x
- 6. The graph of the known quadratic function y = AX2 + BX + C (a ≠ 0) is shown in the figure ① ABC > 0; ② B < A + C; ③ 4A + 2B + C > 0; ④ 2C < 3B; ⑤ a + b > m (am + b) (m ≠ 1 real number) The correct conclusion is () A. 2 B. Three C. Four D. Five
- 7. As shown in the figure, it is known that AB is the chord of ⊙ o, the radius OA = 20cm, ∠ AOB = 120 ° and the area of ⊙ AOB is obtained
- 8. D is the middle of the edge BC of the triangle ABC, De is vertical AC, DF is vertical AB, the vertical feet are e, F, and BF = CE, judge the shape of triangle ABC Is it an isosceles right triangle? Give proof
- 9. As shown in the figure, in RT △ ABC, ab = AC, ∠ a = 90 °, point D is any point of BC, DF ⊥ AB is in F, de ⊥ AC is in E, M is the midpoint of BC. Try to judge what shape △ MEF is and prove your conclusion
- 10. As shown in the figure, in the isosceles triangle ABC, ab = AC, D is a point on the extension line of AB, BD = AB, CE is the center line on waist AB, and verify; CD = 2ce needs specific process
- 11. It is known that, as shown in the figure, in right angle trapezoid ABCD, ad is parallel to BC, ∠ ABC = 90 °, de ⊥ AC is at point F and BC is intersected at point G, which is called ab Verification: BG = FG No picture. Sorry
- 12. As shown in the figure, the vertex angle of the isosceles △ ABC is 50 ° and ab = AC. taking AB as the diameter, make a semicircle and intersect BC at point D and AC at point E BD、 De and The degree of the center angle to which AE is directed
- 13. Let d be a point on the edge BC of △ ABC, and AB2 = ad2 + BD × DC
- 14. As shown in the figure, △ ABC is an equilateral triangle, and points D, e and F are points on the segments AB, BC and Ca respectively, (1) If ad = be = CF, is △ def an equilateral triangle? Try to prove your conclusion; (2) If △ DEF is an equilateral triangle, is ad = be = CF true? Try to prove your conclusion
- 15. As shown in the figure, in the triangle ABC, ∠ 1 = ∠ 2, G is the midpoint of AD, lengthening BG intersecting AC with E.F is a point on AB, CF ⊥ ad is in H (1) Ad is the angular bisector of the triangle Abe; (2) Be is the center line on the side ad of the triangle abd; (3) Ch is the height on the edge ad of the triangle ACD A. 1 B. 2 C. Three D. 0
- 16. It is known that, as shown in the figure, △ ABC is an equilateral triangle, AE = CD, BQ ⊥ ad at Q, be crossing ad at point P, Confirmation: BP = 2pq
- 17. It is known that, as shown in the figure, in △ ABC, ad and AE are the bisectors of the height and angle of △ ABC respectively, if ∠ B = 30 ° and ∠ C = 50 ° (1) Find the degree of ∠ DAE; (2) What is the relationship between ∠ DAE and ∠ C - ∠ B? (no need to prove)
- 18. It is known that AD and AE are the angular bisector and height of triangle ABC respectively, ∠ B = 50 °, ead = 10 ° and ∠ C=____
- 19. As shown in the figure, in △ ABC, the angular bisectors ad, be and CF intersect at point h, passing through point h as Hg ⊥ AC, and the foot perpendicular to g, then ∠ ahe = ∠ CHG? Why?
- 20. As shown in the figure, △ ABC is an equilateral triangle, and ad = be = CF, is △ def an equilateral triangle? Write it out in 20 minutes,