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As shown in the figure, it is known that the straight line AB and CD are cut by the straight line EF. If ∠ BMN = ∠ DNF, ∠ 1 = ∠ 2, then MQ ‖ NP. Why?
It is proved that: ∵ BMN = ∵ DNF, ∵ 1 = ∵ 2 (known), ∵ BMN + ∵ 1 = ∵ DNF + ∵ 2, that is, ∵ PNF = ∵ QMN ∥ MQ ∥ NP
1 as shown in the figure, it is known that AB is parallel to CD, and the straight line EF intersects AB, and CD is equally divided between M, N, MP ∠ EMP, and NQ ∠ MND. Try to judge the position relationship between MP and NQ, and explain the reason
2 as shown in the figure, De is parallel to BC, angle D: angle DBC = 2:1, angle 1 = angle 2, calculate the degree of angle DEB
Figure 1
DE‖BC
The results show that ∠ e = ∠ 1, ∠ D + ∠ DBC = 180 degree
And ∵ - D: ∵ - DBC = 2:1, ∵ - D = 120 ° and ∵ - DBC = 60 °
∠1 = ∠2,∴∠1 = 30°
∠E = ∠1 = 30°
In square ABCD, m, N, P and Q are points on edges AB, BC, CD and Da respectively, and MP is perpendicular to NQ. Are MP and NQ equal
RT, the picture can't be transmitted. It's not the midpoint, any point
I don't know if you're talking about this graph? Now I try to prove that QF is perpendicular to F, and then PE is perpendicular to ab. because the quadrilateral ABCD is a square, QF is perpendicular to BC, PE is perpendicular to AB, so PE = ad = AB = = QF, and PE and QF are perpendicular to each other. MP and QN are perpendicular, and the intersection of MP and QF is a pair of vertex angles. It's easy to conclude that angle 1 equals angle 2, QF is perpendicular to BC, PE is perpendicular to ab, So angle 3 is equal to angle 4, QF is equal to PE. Now we have formed the "angle, side and angle theorem" that two angles are equal on one side. Triangle QFN is equal to triangle PEM, so QN is equal to PM
If there are two points m and N on the straight line a, and Mn = 14cm, the other point q is also on the straight line a, and NQ = 5cm, then MQ =? Fast
If q is on Mn, MQ = mn-nq = 14-5 = 9cm
If q is on the Mn extension line, MQ = Mn + NQ = 14 + 5 = 19cm
in summary
MQ = 9cm or 19cm
RELATED INFORMATIONS
- 1. As shown in the figure, CD ‖ EF, ∠ C ＋ f = ∠ ABC, verification: ab ‖ GF
- 2. As shown in the figure, there are free moving metal rods PQ and Mn on the two horizontal smooth guide rails. When PQ moves under the action of external force, Mn moves to the right under the action of magnetic force, the movement of PQ may be () A. Uniform acceleration to the right B. uniform acceleration to the left C. uniform deceleration to the right D. uniform deceleration to the left
- 3. Given that B is a point on line AC, M is the midpoint of line AB, n is the midpoint of line AC, P is the midpoint of Na, q is the midpoint of Ma, find Mn: PQ Because PQ = ap-aq = an ﹣ 2-AM ﹣ 2 = (an-am) ﹣ 2 = Mn ﹣ 2 So Mn △ 2 = PQ Mn = 2pq So Mn: PQ = 2:1
- 4. Known: as shown in the figure, in rectangular ABCD, points E and F are on the edge of AD, CE and CF intersect with BD at points m, N, AE = EF = FD = 4cm, ab = 16cm, respectively, to find the length of Mn
- 5. In the quadrilateral ABCD, ab = CD, e and F are the midpoint of BC and ad. the extension lines of Ba and EF intersect at m, the extension lines of CD and EF intersect at n, proving that angle ame is equal to angle dne
- 6. In the parallelogram ABCD, e is the midpoint of diagonal AC, EF is perpendicular to F, angle B = 60 degrees, ab = 4, angle ACB = 45 degrees, find the length of DF
- 7. As shown in the figure, in square ABCD, e is on CD, and AE = EC + BC, M is the midpoint of CD, and the proof is: ∠ BAE = 2 ∠ dam The map address is D: / / my documents / doc1.mht
- 8. In rectangular ABCD, point m is the midpoint of CD, ab = 8cm, BC = 10cm. Fold the rectangular ABCD so that a and M coincide. Crease EF intersects ad at point E, BC at point F, Find the length of AE
- 9. In the isosceles trapezoid ABCD, the diagonal AC ⊥ BD of ad ∥ BC is perpendicular to o, AE and DF, and the perpendicular feet are e and F. if ad = a, BC = B, the perimeter of quadrilateral aefd can be calculated
- 10. Given that the two diagonals of the diamond are 6 and 8 respectively, what is the perimeter of the diamond?
- 11. As shown in the figure, the straight lines AB and CD are cut by the straight line EF. If the apposition angle ∠ 1 = ∠ 3, is the internal stagger angle ∠ 2 equal to ∠ 3? Is the inner corner ∠ 3 and ∠ 5 complementary? Please give reasons
- 12. If ab ∥ CD, CD ∥ EF, EF ∥ GH are known, what is the positional relationship between AB and GH, and explain the reason A——B C———D E————F G—————H
- 13. AB + CD + EF + GH = III. which number is eliminated in 0-9? (competition) why? A letter stands for a number
- 14. It is known that the line AB and CD intersect at O, OM ⊥ CD, the perpendicular point is O, OA bisects ∠ MOE, and ∠ BOD = 28 ° to find the degree of ∠ AOM ∠ COE ∠ BOE
- 15. As shown in the figure, the straight lines AB, CD and EF all pass through point O, and ab ⊥ CD and og bisect ∠ BOE. If ∠ EOG = 25 ∠ AOE, calculate the degrees of ∠ EOG, ∠ DOF and ∠ AOE
- 16. For a car with a mass of M = 1000kg, the maximum speed V1 = 12m / s when driving on a straight road at rated power, and the maximum speed V2 = 8m / s when driving on a slope with an increase of 1m for every 20m. Assuming that the friction force on the car is equal under any condition, G is taken as 10m / S2, the following formula is obtained (1) The size of friction force; (2) What is the rated power of automobile engine; (3) The maximum speed a car can reach when going down the slope
- 17. On a flank slope with an inclined angle of 60 degrees, climb along the road with an angle of 30 degrees to the horizontal line of the slope toe for 100 meters How many meters
- 18. The slope angle of a hillside is 30 degrees. If one kilometer goes along a straight road with 45 degrees to the slope, the slope will rise A. 250 with 2m b.250 with 3M c.250 with 6m d.500m
- 19. It is known that the angle between line AB and plane a is 30 degrees, the angle between line AC and plane a is 6O degrees, ab = 6cm, AC = 8cm, and the projective ab 'and AC' of oblique line AB and AC in plane a are perpendicular to each other?
- 20. Is the dihedral angle range [0, π / 2], or is the plane angle range [0, π / 2)? Is a dihedral angle a corner? Does it have scope, What is the relationship with the plane angle range?