Isosceles & Equilateral Triangles, Study notes of Geometry

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ISOSCELES TRIANGLES AND

MIDSEGMENTS TRIANGLES

Section 4.

REMEMBER: EQUILATERAL TRIANGLE

A triangle with all three sides of equal length

and all 3 angles of equal measure is called

an equilateral triangle.

(Note: All the angles will be 60°.)

Y

X Z

ISOSCELES TRIANGLES

Explain why ∆𝑅𝑆𝑇 is Isosceles.

T

U

R

V

S

W

PROPERTIES OF ISOSCELES TRIANGLES

If 2 sides of a triangle are congruent, then their opposite angles are congruent. Similarly, if 2 angles of a triangle are congruent, then their opposite sides are

congruent.

Example: Find the values of the variables

x 41 ° y

PROPERTIES OF ISOSCELES TRIANGLES (CONT’D)

Example: Find the value of x

PROPERTIES OF ISOSCELES TRIANGLES (CONT’D)

Example: Find the value of the x

THE BISECTOR OF AN ISOSCELES TRIANGLE

Example: Find the values of the variables L M N O y x 6 3

MIDSEGMENTS OF TRIANGLES

The midsegment of a triangle is the segment connecting the

midpoints of two sides.

If Q is the midpoint of 𝑌𝑍 & S is the

midpoint of 𝑋𝑍. Then, 𝑄𝑆 is a

midsegment of ∆𝑋𝑌𝑍.

MIDSEGMENTS OF TRIANGLES

Example: Find the measure of each. EB= BC= AC= 𝑚∠𝐸𝐷𝐶 = 𝑚∠𝐸𝐷𝐶 =

E and B are midpoints

MIDSEGMENTS OF TRIANGLES

Example: Find the length of each. HJ= JK = FG=

H, J, and K are midpoints.

MIDSEGMENTS OF TRIANGLES

Example: In^ ∆𝑋𝑌𝑍 , M, N,^ and^ P^ are midpoints. The perimeter^ of^ ∆𝑀𝑁𝑃^ is 60. Find^ NP and YZ.

SECTION 4.1 ASSIGNMENT

Worksheet 4.