Current location - Training Enrollment Network - Mathematics courses - The finale of junior one mathematics and its answers.
The finale of junior one mathematics and its answers.
hope this helps

1. It is known that the vertex of the equilateral triangle ABC is placed at point A, and the triangle rotates around point A, and both sides of the 60-degree angle intersect with the bisector of the straight line BC and point D and ∠ACB respectively at point E. (1) When D and E are on the bisector CM of BC and ∠ACB respectively, as shown in figure/kloc-. (2) When D and E are on straight lines BC and CM respectively, as shown in Figures 2 and 3, what is the quantitative relationship among DC, Ce and AC? Please write the conclusion directly. (3) In Figure 3, when ∠ AEC = 30 and CD=4, find the length of CE.

answer

Proof: Because EAD = BAC = 60.

So ∠ bad = ∠ EAC

It is also a regular triangle ABC, so AC = AB.

Because ∠ ACB = 60 and CM is the bisector of ∠C,

So ∠ ace =1/2 (180-60) = 60.

That is ∠ ace = ∠ ACB.

So triangle ABD and triangle ACE are congruent.

So db = ce, so DC+ce = CD+BD = BC = AC.

2) Figure 2: DC-CE = AC

Figure 3: CE-CD = AC

All the proofs are to prove the congruence (ASA) of triangle ABD and triangle ACE.

3) Because ∠ ACM = 60 = ∠ B

∠BAD=∠CAE,AC=AB

So triangle ABD and triangle ACE are congruent.

So ∠ ADB = ∠ AEC = 30.

Because ∠ b = 60

So triangle ABD is a right triangle with an angle of 60,

So BD = 2ab, so BC = DC = 4.

So ce = 8

2./view/8 afab 0 c 38 BD 63 186 BCE BBC 43 . html

The content of this website is the title. Do it first, and you won't ask questions.

In fact, you can go to Xinhua Bookstore to buy a slightly more difficult book, or you can.