![](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>)
Triangle ABC, AC = BC, angle c = 90 degree, point D on BC, fold triangle ACD along ad, point C just falls on point E on AB, if AB = 6cm Finding the perimeter of triangle deb The picture can't be sent out
Because AC = BC ∠ C = 90 ° AB = 6
So AC = BC = 6 △ radical 2 = 3 radical 2
Because the triangle ade is folded by ACD
So CD = De, AC = AE = 3, radical 2
So be = ab-ae = 6-3 radical 2
Because CD + BD = BC = 3 radical 2 CD = de
So de + BD = BC = 3 change sign 2
So C triangle DEB = be + BD + de = 6
The proposition "if a = B, then a ⊆ B" and its converse proposition, no proposition, converse no proposition, among these four propositions, the number of true propositions is______ ．
Because the original proposition "if a = B, then a ⊆ B" is true, so the inverse no proposition is true, and the inverse proposition: "if a ⊆ B, then a = B", this conclusion is not true, so the inverse proposition is false, so the no proposition is also false, so the answer is 2
If a or B, what are the inverse proposition, negative proposition and inverse negative proposition of C?
Inverse proposition: if C, then a or B
No proposition: if it is not a and B, then it is not C
You have no proposition: if not C, then not a and not b
As shown in the figure, it is known that in △ ABC, ab = AC, the vertical bisector De of AB intersects AC at point E, and the vertical bisector of CE just passes through point B and intersects AC at point F. the degree of ∠ A is calculated
∵ ABC is an isosceles triangle, ∵ ABC = ∠ C = 180 − A2 ①, ∵ De is the vertical bisector of line AB, ∵ a = ∠ Abe, ∵ CE's vertical bisector just passes through point B and intersects with AC at the point, we can see that ∵ BCE is an isosceles triangle, ∵ BF is the bisector of ∠ EBC, ∵ 12 (∠ ABC - ∠ a) + ∵ C = 90 °
As shown in the figure, △ ABC, the vertical bisector De of AC intersects AC at point E and BC at point D. if AB = DC, ∠ C = 35 °, calculate the degree of ∠ B
Connect ad, ∵ De, divide AC vertically, ∵ - Da = DC, ∵ - C = 35 °, ∵ - DAC = - C = 35 °, ∵ - ADB = - DAC + C = 35 ° + 35 ° = 70 °, ∵ AB = DC, ∵ - AB = ad, ∵ - B = - ADB = 70 °
In the triangle ABC, ab = AC, the acute angle formed by the intersection of the vertical bisector of AB and the line where AC is located is 40 degrees, then what is the degree of angle B
The answer is 65 degrees or 15 degrees
Because AB = AC, the vertex angle is a,
When the angle a is less than 90 degrees, the vertical bisector of AB intersects AC, e intersects AB at F
Triangle AFE is a right triangle, angle a = 90-40 = 50 degrees, angle B = (180-50) / 2 = 65 degrees
When angle a is greater than 90 degrees, angle a = 180 - (90-40) = 130 degrees, angle B = (180-130) / 2 = 15 degrees
As shown in the figure, in the isosceles right triangle ABC, the bisector of the angle BAC intersects at the point E, EF ⊥ AC at the point F, FG is perpendicular to ab at the point G;
AE is the bisector of ∠ fab, EF ⊥ AF, and AE is the common edge of △ AFE and △ Abe,
∴Rt△AFE≌Rt△ABE（AAS）,
∴AF=AB．①
In RT △ AGF, ∵ ∠ fag = 45 °,
∴AG=FG,
∴AF2=AG2+FG2=2FG2．②
AB2 = 2fg2 from ① and ②
As shown in the figure, in △ ABC, ∠ ACB = 60 ° AC > BC, and △ ABC ', △ BCA', △ cab 'are equilateral triangles outside the △ ABC shape, while point D is on AC
And BC = DC
1. Prove that: △ c'bd ≌ △ b'dc;
2. Proof: △ ac'd ≌ △ db'a
3. What conclusions can you draw from the relationship between area and size of △ ABC, △ ABC ', △ BCA', △ cab '?
(1) ∵△ cab 'is an equilateral △
∴B'C=AC,∠B'CA=∠ACB=60°
∵DC=BC
The ∧ BCD is equilateral
∴DC=BD
∴△B'DC≌△ABC (SAS)
∴B'D=AB=C'B,∠B'DC=∠ABC
∵∠CBD=∠ABC'=60°
∴∠CBD+∠ABD=∠ABC'+∠ABD
That is, ABC = c'bd
∴∠B'DC=∠C'BD
∴△C'BD≌△B'DC (SAS)
(2) From (1), we can get △ c'bd ≌ △ b'dc
∴B'C=C'D,B'D=C'B,∠CB'D=∠DC'B
∵∠AB'C=∠AC'B=60°
∴∠AB'C-∠CB'D=∠AC'B-∠DC'B
That is ∠ ab'd = ∠ dc'a
∵B'C=C'D=AB',B'D=C'B=C'A
∴△AC'D≌△DB'A (SAS).
Sorry, (3) I don't know~
If AC = 2.4cm, BC = 1.5cm, then the area of △ AEC is______ ．
∵∠ C = 90 °, AC = 2.4cm, BC = 1.5cm, ∵ s △ ABC = 12ac · BC = 12 × 2.4 × 1.5 = 1.8cm2, ∵ CE is the middle line of △ ABC, ∵ AEC area = 12S △ ABC = 12 × 1.8 = 0.9cm2
In △ ABC, ad and CE are the middle line, ∠ bad = ∠ BCE. Please guess the shape of △ ABC and prove it
ABC is an isosceles triangle
It is proved that: bad = BCE
∠ABD=∠CBE
So, △ abd ~ △ CBE
BD/BE=AB/CB
Ad and CE are the middle line
So AB / CB = BD / be = BC / ab
AB^2=BC^2
AB=BC
ABC is an isosceles triangle
RELATED INFORMATIONS
- 1. Original proposition: √ a ＞ B, then a ＞ B (write its inverse proposition, no proposition, inverse no proposition)
- 2. If a = B, then a = B (fill in "true" or "false") proposition, its inverse proposition is, it is (fill in "true" or "false") proposition
- 3. If three line segments a, B and C satisfy a square = C square - b square, is the triangle formed by these three line segments a right triangle? Why? Please explain the process and reasons,
- 4. Let a and B be the lengths of two right angles of a right triangle and (A2 + B2) (3 under the root of A2 + b2-4) = - 12, then the value of A2 + B2 is Thank you for your correct answer!
- 5. Write down the inverse proposition of the following proposition, and judge whether it is true or false. 1. The same position angle is equal, and the two lines are parallel. 2. The inner stagger angle is equal, and the two lines are parallel
- 6. The converse proposition of the proposition "equal angle, parallel two lines" is as follows:______ ．
- 7. If △ ABC ≌ △ DEF is known, if △ ABC and perimeter are 38, ab = 14, AC = 8, try to find the length of EF respectively 5 yuan fortune reward
- 8. ① In △ ABC and △ def, AB / de = BC / EF = AC / DF = 4, find the perimeter ratio of △ def, M: n = 1 / 7:1 / 6, N: T = 1 / 4:1 / 3, then M: n: T =? ① In △ ABC and △ def, AB / de = BC / EF = AC / DF = 4, find the perimeter ratio of △ def ② M: n = 1 / 7:1 / 6, N: T = 1 / 4:1 / 3, then M: n: T =?
- 9. As shown in the figure, in the plane rectangular coordinate system, the length of ABC side of equilateral triangle is 3 / 2, and BC side is on the negative half axis of X, e (0, a), f (B, 0) If the equilateral triangle ABC starts from the origin O and moves to the left, when B and f coincide, AC intersects EF at N and the length of CN is calculated (2) In ABC motion of equilateral triangle, AB intersects EF with M. when the area of triangle AOM is √ (3) / 2, m coordinate is obtained
- 10. For the regular triangle ABC whose side length is 6, establish the right angle coordinate system and write out the coordinates of each point
- 11. As shown in the figure, in RT △ ABC, ∠ C = 90 °, AC = 4cm, BC = 3cm, now fold △ ABC to make vertex A and B coincide, then the length of crease De is () cm A. 52B. 154C. 158D. 5
- 12. As shown in the figure, in △ ABC, de ‖ BC, ad: DB = 3:2 (1) find the value of DEBC; (2) find the value of bced & nbsp; of s △ ADEs quadrilateral
- 13. RT, in triangle ABC, ab = AC = 10, point D on BC, de parallel AC, DF parallel AB, find the perimeter of quadrilateral AEDF
- 14. It is known that: as shown in the figure, point D is a point on the edge AC of △ ABC, passing point D makes de ⊥ AB, DF ⊥ BC, e and F are perpendicular feet, then passing point D makes DG ∥ AB, intersecting BC at point G, and de = DF. (1) prove: DG = BG; (2) prove: BD bisects EF vertically
- 15. As shown in the figure, in △ ABC, ∠ B = 90 °, ab = 3, AC = 5, fold △ ABC so that point C coincides with point a, and the crease is De, then the perimeter of △ Abe is______ ．
- 16. In triangle ABC, AF: FB = BD: DC = Ce: AE = 3:2, be, CF and ad intersect point igh on BC, AC and ab respectively, and the area of IgH is 1
- 17. In the triangle ABC, BD.CD They are the diplomatic bisector of angle ABC and angle ACB
- 18. As shown in the figure, in △ ABC, BD and CD divide ∠ ABC and ∠ ACB equally, and try to explain ∠ d = 90 ° + & # 189; ∠ a
- 19. As shown in the figure, BD is the extension of the intersection of the middle line AE ⊥ BD on the edge AC of △ ABC at the point ECF ⊥ BD. be + BF. = 2bd is proved at the point F It's sloppy
- 20. In ABC, BD is the inner bisector of angle B, CE is the outer bisector of angle c, AF is perpendicular to BD, Ag is perpendicular to CE, FG and ABC?