**Calculating with triangles**

Tính toán liên quan đến tam giác

BÀI VIẾT LIÊN QUAN:

- The name of all triangles
- Properties of triangles – Part 1
- Properties of triangles – Part 2
- Vocabulary angles
- Vocabulary of Fractions

*The base angles of an isosceles triangle are equal.*

If *a *= *b, *then *x *=
*y*

*If the base angles of a triangle are equal, the triangle is isosceles.*

If *x *= *y, *then *a *=
*b*

*The measure of an exterior angle is equal to the sum of the measures of the remote interior angles.*

*l is a straight line.*

*Then, x = y + z*

*In a triangle, the greater angle lies opposite the greater side.*

If a < b, then y < x

If a < b, then y < x

*Similar Triangles*

If ΔABC ~ ΔDEF, then

m∠A = m∠B

m∠B = m∠E

m∠C = m∠F

and * *

**The sum of the interior angles of a triangle is 180 degrees.**

m∠A + m∠B + m∠A = 180º

*The area of a triangle is one-half the product of the altitude to a side and the side.*

Area of △*ABC *=

*Note: *If m∠A = 90º

Area also =

*In a right triangle*

*c*^{2} = *a*^{2} + *b*^{2}

and *x*°+ *y*° = 90°

*Memorize the following standard triangles*

** The sum of the lengths of two sides of a triangle is greater than the length of the third side.** (This is like saying that the shortest distance between two points is a straight line.)

*a *+ *b *>
*c*

*a *+ *c *>
*b*

*b *+ *c *> *a *

**Example 1**

In the diagram below, what is the value of *x*?

(A) 20

(B) 25

(C) 26

(D) 45

(E) 48

**Example
2**

If Masonville is 50 kilometers due north of Adamston and Elvira is 120 kilometers due east of Adamston, then the minimum distance between Masonville and Elvira is

(A) 125 kilometers

(B) 130 kilometers

(C) 145 kilometers

(D) 160 kilometers

(E) 170 kilometers

**Example 3**

In triangle *ABC, *if *a *>
*c, *which of the following is true?

(A) BC = AC

(B) AB > BC

(C) AC > AB

(D) BC > AB

(E) BC >AC

**Example
4**

The triangle above has side *BC *=
10, angle *B *= 45°, and angle *A *= 90°. The area of the triangle

(A) is 15

(B) is 20

(C) is 25

(D) is 30

(E) Cannot be determined.

**Example
5**

In the figure above, what is the value
of *x*?

(A) 30

(B) 40

(C) 50

(D) 80

(E) 100

**Example
6**

Which of the following represents all
of the possibilities for the value of *a *in the figure above?

(A) 1 < *a *< 9

(B) 4 < *a *< 5

(C) 0 < *a *< 9

(D) 4 < *a *< 9

(E) 5 < *a *< 9

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