2020 Community Worker Examination Preparation Guide: Essential Knowledge of Triangles in Geometry Problems

Introduction

The Tianjin Community Worker Examination Network provides candidates with practice test skills "Essential Knowledge of Triangles in Geometry Problems" to help candidates enrich their practice test preparation knowledge and analyze question-answering techniques. . More exciting content is available in Community Worker Recruitment!

The examination of geometric problems focuses on personal spatial abilities, and many people do not use their spatial abilities very well, so they have difficulty solving geometric problems. The basis of geometric problems is to memorize relevant formulas and properties, and triangles are an important test point in geometric problems, so they must be mastered. Next, I will take all candidates to study geometry problems.

1. Formulas and properties

There are not many formulas involved in triangles, among which area is easier to solve. Area = (base?height)?2, and all three sides can be bases. It should be understood that half the product of the heights of the three sides is the area of ??the triangle. For right triangles, you also need to remember the formula for the Pythagorean Theorem.

The basic property of a triangle is the three-sided relationship: the sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.

Example 1 has two wooden rods with lengths of 4cm and 9cm respectively. If you want to nail a triangular wooden frame, there are currently five wooden rods with lengths of 3cm, 6cm, 11cm, 12cm and 13cm to choose from. , there are several methods to choose from ( )

A.1 B.2 C.3 D.4

Answer C. Analysis: According to the relationship between the three sides of the triangle, the third wooden stick is >5, and <13. Then 6, 11, and 12 among them are consistent. So choose C.

A property often tested in exams is the similarity of triangles: corresponding sides of similar triangles are proportional and corresponding angles are equal. However, unlike the college entrance examination, the practical examination does not examine proof, but focuses on application.

It is known in Example 2 that DE∥BC, E is the trisection point of AC, and the length of DE is 5cm. What is the length of BC?

A.10 B.15 C.20 D.25

Answer B. Analysis: Triangle ADE is similar to triangle ABC, E is the trisection point, then AE/AC=1/3, then the similarity ratio is 1/3, so DE/BC=1/3, BC=3DE=15. The answer is B.

After analyzing the questions, you will find that the geometry questions focus on discovering geometric laws and then solving them based on relevant properties. Similarity of triangles is a basic knowledge, and all candidates must be proficient in it.

2. Classic examples

Example 1 A right triangle has the longest side 15cm and the shortest side 9cm. How much greater is the area of ??the triangle than the perimeter? ( )?

A.18 B.54 C.36 D.27

Answer A. Analysis: First of all, this triangle is a right-angled triangle. Its longest side is 15, and its shortest side is 9, which means that the length of its hypotenuse is 15. One right-angled side is 9. Using the Pythagorean theorem, we can know that the length of the other right-angled side is 12. The area of ??the triangle is (12?9)/2=54; the perimeter of the triangle is: 15+12+9=36; 54-36=18, so choose A. for this question.

Example 2 As shown in the figure, the two diagonals AD and BC of the trapezoid ABCD are compared to point O. It is known that the area of ??the triangle ABO is 1, and AB:CD=1:2, find the trapezoid ABCD What is the area?

A.4 B.7 C.9 D.11