Congruent distance, a method of measuring the distance of a triangle

This is a method of achieving the purpose of ranging by transferring the target at an equal distance.

Thales, the first natural philosopher in ancient Greece, used the shadow of the sun to measure the height of the pyramid.

His method is to measure the length of a pole b, the shadow length of the pole a, and the shadow length of the pyramid c at the same time, and the height of the pyramid = bc a.

By extension, there is no need for conversion when using congruent triangle ranging, and the principle is the same.

For example, if I want to measure the distance from a building on the other side of the river to my foothold, I can't cross the river. Method:

Facing the building, adjust the brim of the hat so that the line of sight falls right on the bottom of the building, turn the direction so that the line of sight falls on a certain point on the shore where you are, so that you can roughly measure the distance by walking backwards. Determining the object point twice is simplified to the distance, the height of the person, and the line of sight to form two congruent triangles, which is congruent ranging. Complete.

There are methods for measuring triangular congruent distances: similarity distance, angular distance, marker distance, and cliff distance.

1. Similar distance method: Using the principle of similar triangles, first establish a triangle similar to them between two positions (that is, a triangle with the same proportion as the real size), and then compare the side length ratio of the two triangles to find the true distance. This method requires knowing a known length, such as the actual distance on a map or the height of a marker.

2. Angular distance method: using the principle of congruent triangles, measure an angle from two points to the target point, and then use trigonometric functions to calculate the distance from the two positions to the target point, and then use the Pythagorean theorem to find the real distance.

3. Celery nucleus marker distance method: find the marker around the target point and measure its height, use the distance between the target point and the marker as the baseline, use the trigonometric function to calculate the distance from the target point to the baseline, and then use the Pythagorean theorem to find the real distance.

4. Cliff distance method: use the edge of the cliff as a point to build a triangle and compare it with the real size ratio to find the distance. This method is suitable for distance measurement at cliff or valley locations. It is necessary to know the measurement data of the cliff height and edge angle.

The principle of congruent distance measurement of triangles

The principle of distance measurement of triangles is based on the property that the corresponding sides of congruent triangles are equal. This principle is called the property of congruent triangles, i.e. if the three sides of two triangles are equal respectively, then they are congruent. So, if two triangles are congruent, then their corresponding sides are equal.

According to this principle, when we want to measure the distance between two triangles on the map, we can first use the three corners marked on the map to determine that the two triangles are congruent. Since these two triangles are congruent, their three sides must also be equal, i.e., the sides of any two matching fingers in the triangle are equal in length.

Therefore, we can use the known length of an edge, and then substitute the length of this side into another triangle to calculate the length of the corresponding side through the principle of equality of the corresponding edges, so as to find the length of the three sides of the other triangle. Next, in these two identical triangles, we can calculate the desired distance value by using the Pythagorean theorem.

The purpose of using triangular congruent distance measurement is to convert the distance equivalence of two points that cannot be reached into the distance between two points that can be measured directly, and the theoretical basis is that the corresponding sides of congruent triangles are equal

So the answer is: the corresponding sides of a congruent triangle are equal

Proof: AC=DF

ac-fc=df-fc

af=cd in the manuscript key bridge amf and dnc:

A= D=30°,AF=CD, MFA= NCD=90° AMF Plum-dNC (ASA Corner Corner).

This diagram is an example, point m is point A and point n is point B. Make it next to the lake, make mq, mp and o points, and make on=op, om=oq, angle nom=angle poq, so according to the saas triangle congruence determination theorem, mn=pq, as long as pq is measured.

Solution: 1. Take DF=CB on DB from point D, so that point F can be determined.

2. In the same way, take de=ca from point d, then point e can also be determined.

Correct aa'=bb'o is the midpoint.

then OA=OA'=ob=ob'

boa≌△b'oa'Corner edges.

So ab=a'b'

That's right, the reason is that the triangle is congruent.