What kind of conditions do you need to prove the diamond in the eighth grade second volume mathematics test (PEP Edition)? For example, △ ABC and △ CDE are equilateral triangles, points E and F are on AC and BC respectively, and ef ‖ ab (1) verification: the quadrilateral efcd is a diamond; (2) let CD = 4, find the distance between D and F

What kind of conditions do you need to prove the diamond in the eighth grade second volume mathematics test (PEP Edition)? For example, △ ABC and △ CDE are equilateral triangles, points E and F are on AC and BC respectively, and ef ‖ ab (1) verification: the quadrilateral efcd is a diamond; (2) let CD = 4, find the distance between D and F

Because: triangle ABC and triangle CDE are equilateral triangles, so: angle ACB = angle DCE = angle d = angle Dec = angle a = angle B = 60 degrees AB = BC = Ca, CD = de = EC, triangle CEF is also equilateral triangle, CD is parallel to AB, CD is parallel to EF, De is parallel to BC, efcd is parallelogram, because: CD = de = CE = CF = EF quadrilateral

Answers to the final comprehensive examination paper of Chinese innovative exercises in the eighth grade volume II of people's Education Press

1.D 2.C 3.B 4.B 5.C 6.A
2、 Ancient poetry reading and accumulation (22 points)
（1） Read the following ancient poems and complete questions 7-8. (4 points)
7.C 8.B
（2） Read the following classical Chinese and complete questions 9-13. (10 points)
9.B
10. (1) some people (2) this
11. The villain was afraid of him, so he lured him with money. He looked very serious and didn't look at him
Don't be happy with things, don't be sad with yourself
He is clean and honest. The emperor knows his character and protects him
（3） Accumulation of ancient poetry. (8 points)
14. (1) he died in the Carpinus. (2) he turned into Acacia tears. (3) he sailed a thousand sails by the side of the sunken boat. (4) he looked at the grass from afar, but he was not afraid of the floating clouds. He was at the highest level. (6) when the wind broke the waves, he would fly the clouds to help the sea
3、 Modern reading (30 points)
（1） Read the following and complete questions 15-19. (17 points)
15. "I" firmly concluded that this row of camphor trees would die. Reasons: this row of camphor trees is lifeless; the soil where they are planted is not fertile and the water content is low; many days have passed since the tree planting day, and the temperature has been so high for several days without rain
sixteen
time
The shape of trees
My mood
Two weeks ago
Bare commander, lifeless
Doubt, obstinacy and pessimism
Two weeks later
Sprout green, bloom green
Surprise, guilt, love
17. Summarize the full text, point out the center, make the finishing point, and sublimate the theme. Inspiration: be tolerant of other people's shortcomings and shortcomings, and look at their future with the perspective of development; support and care for others, rather than categorically deny them
18. (1) example: the word "bare rod commander" adopts personification rhetoric, vividly showing the straight and bare shape of camphor tree when it is planted. The words "not so much to say", "not to say", "not to say" highlight the author's disappointment with the shape of camphor tree
(2) Examples: "a trace of green", "a touch of green" and "a piece of green". There is only one word difference between the phrases, but it describes the changing process of camphor tree. The words are concise and to the point, which shows the author's attention to camphor tree
19. Example: Mo Yan is in adversity and is discriminated against by others, but like the camphor tree in the article, he constantly overcomes difficulties, displays his brilliance tenaciously, blooms his beauty, explores boldly on the road of literature, and finally becomes the Nobel Prize winner of literature
（2） Read the following and complete questions 20-23. (13 points)
20. First, point out the object of the article; second, use analogy to stimulate readers' interest in reading; third, vividly explain the "safety and energy saving" characteristics of foamed cement
21. ① flame retardant; ② high compressive strength, no deformation, strong crack resistance; ③ safety and environmental protection; ④ long service life; ⑤ good thermal insulation and sound insulation effect
22. Examples. The fire cases of several buildings in recent years are used to illustrate that the fire is caused by the spark ignition of flammable thermal insulation materials, which need to be banned and replaced urgently, thus leading to the object of this paper foam cement
23.（1）× （2）× （3）√
Comprehensive learning and writing (56 points)
(1) Examples: ① the transportation and tourism departments should release the forecast of roads and scenic spots in time to guide people to travel; ② tourists should pay attention to relevant information in time and make good travel plans to avoid traveling in congested periods and sections; ③ the state introduces the daily paid vacation degree to facilitate ordinary people to flexibly choose travel time and sections; ④ people with travel plans should choose nearby tourist destinations
(2) Clearly, the head teacher also wants us to have a happy summer vacation, otherwise he or she will not organize the students to give advice. At present, giving up the travel plan is not because of the head teacher, but because the superior has written regulations. I think this is also out of the consideration of collective safety, so please understand the head teacher
Remember to judge the best!

Zhangjiakou 2011-2012 academic year first semester junior high school final academic level test

It is known that in rectangle ABCD, ad = 6, ab = 4, points E and F are the points on BC and ab respectively, and points g and H are the midpoint of De and EF respectively

How to prove that the sum of the three interior angles of a triangle is 180 degrees?

1. Fold the three angles of a triangle inward, and the three angles just form a flat angle, so it is 180 degrees. 2. Make a parallel line on the opposite side of a triangle at a vertex, and prove it with an internal stagger angle. 3. Make a triangle ABC, pass through point a, make a straight line EF parallel to angle BC, EAB = angle B, FAC = angle c, EAB + angle fac + angle BAC = 180, BAC + angle B + angle c =

If the sum of the internal angles of a triangle is 180 degrees, the first angle is three times the second angle, and the third angle is 15 degrees larger than the second angle
1: So what's the second angle? What's the other two angles?

According to the meaning of the title, set the second angle as X degree
According to the known conditions, the first angle is 3x degrees, and the third angle is (x + 15) degrees
Because the sum of the internal angles of a triangle is 180 degrees
So if x + 3x + (x + 15) = 180, then x = 33 degrees
So the second angle is 33 degrees, the first is 3x = 99 degrees, and the third is x + 15 = 48 degrees

If the first angle is three times the second angle and the third angle is 15 degrees larger than the second angle, then

∠1=99° ∠2=33° ∠3=48°
Let ∠ 2 = X
Then 3x + X + (x + 15) = 180
5x=180-15
5x=165
x=33

The sum of the internal angles of a triangle is equal to 180 degrees. It is known that the first internal angle of a triangle is equal to three times of the second internal angle, and the third internal angle is 15 degrees larger than the second internal angle. What is the degree of each angle?

Let the second internal angle be x, the first internal angle be 3x, the third internal angle be x + 15 °, the sum of internal angles of ∵ triangle be 180 °, and the solution be x = 33 °, the first internal angle be 3x = 99 °, the second internal angle be 33 ° and the third internal angle be 48 °

If the ratio of the three inner angles of a triangle is 1:2:3, then the ratio of the lengths of the opposite sides is ()
A. 1：2：3B. 1：3：2C. 1：4：9D. 1：2：3

Let the minimum angle be α, then the three inner angles are α, 2 α and 3 α respectively, and then from α + 2 α + 3 α = π, α = π 6 can be obtained, so the values of the three inner angles are π 6, 2 π 6 and 3 π 6 respectively. Therefore, according to the sine theorem, the ratio of the corresponding three sides of the triangle is sin π 6: sin 2 π 6: sin 3 π 6 = 12:32:1 = 1:3:2

Why is "in a right triangle, the sum of squares of two sides equals the square of the third side" wrong

It's wrong to point out which side is a right angle. The square of the hypotenuse of a right triangle is equal to the sum of the other two squares,

How to prove that the square sum of the areas of the sides of a triangular pyramid with three right triangle faces is equal to the square of the area of the bottom
If you know the answer, please generously leave your message

If three sides are right triangles, only three sides are right angles. Let the Mitsubishi cone be a- BCD.AB.AC Ad is perpendicular to each other. In triangle ABC, make AE vertical BC, perpendicular foot is e, connect de. the theorem of three perpendicular lines is easy to get, and De is vertical BC. The square sum of three side areas = (AB ^ 2 * ad ^ 2 + AC ^ 2 * ad ^ 2 + BC ^ 2 * AE ^ 2) / 4