Transcript Section 5-4 Equilateral and Isosceles Triangles Gordonx

BAT
Geometry
POINTS, LINES AND PLANES
PreQuiz 5A
State whether the transformation appears to be congruent
or similar. Also determine which composition of
transformations occurred. Black pre image → grey image.
Congruent or similar?
Transformations:
1.
2.
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
What is required to show that
two triangles are congruent.
Learning Objective: Students will be able to use
properties of isosceles and equilateral triangles.
Learning Target 4E I can determine a triangle to be
isosceles or equilateral and use the Base Angles
theorem to find missing sides or angles.
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
Page 140
Legs – the two equal sides of an isosceles triangle.
Vertex Angle – the angle between the two equal sides.
Base – the third side of the triangle.
Base Angles – the other two angles.
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
Page 140
Theorem 5.6 Base Angles Theorem
If two sides of a triangle are congruent, then the angles
opposite them are congruent. If 𝑨𝑩 ≅ 𝑨𝑪 then ∠𝑩 ≅ ∠𝑪.
Theorem 5.7 Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides
opposite them are congruent. If ∠𝑩 ≅ ∠𝑪 then 𝑨𝑩 ≅ 𝑨𝑪.
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
Page 141
Corollary 5.2 Corollary to the Base Angles Theorem
If a triangle is equilateral, then it is equiangular.
Corollary 5.3 Corollary to the Converse of the Base Angles
Theorem.
If a triangle is equiangular, then it is equilateral.
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
Page 141
In Exercises 1-4, complete the statement. State which
theorem you used.
1. If 𝑁𝐽 ≅ 𝑁𝑀, then ∠_______ ≅ ∠_______
2. If 𝐿𝑀 ≅ 𝐿𝑁, then ∠_______ ≅ ∠_______
3. If ∠𝑁𝐾𝑀 ≅ ∠𝑁𝑀𝐾, then _______ ≅ _______
4. If ∠𝐿𝐽𝑁 ≅ ∠𝐿𝑁𝐽, then _______ ≅ _______
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
Page 142
In Exercises 5 and 6, find the value of x.
Geometry
POINTS, &
LINES
AND PLANES
5-4 Equilateral
Isosceles
Triangles
Page 142
In Exercises 7 and 8, find the value of x and y.