Bell work Use the diagram to find x. b||c. a 80° b c x + 30

Bell work Use the diagram to find x. b||c. Alternate exterior angles are congruent. a 80° b c x + 30

Bell work Use the diagram to find x. b||c. Alternate exterior angles are congruent. a 80° b c So, x + 30 = 80° x + 30 = x = 50°

5 - 3 Triangles Find unknown angles and identify possible side lengths in triangles.

The figure below shows two parallel lines m and n, and a triangle. m n What is the sum of angles 4, 1, and 5? 2. Name an angle with the same measure as angle Name an angle with the same measure as angle 5.

The figure below shows two parallel lines m and n, and a triangle. m n What is the sum of angles 4, 1, and 5? 2. Name an angle with the same measure as angle 4. Angle 2 3. Name an angle with the same measure as angle 5.

The figure below shows two parallel lines m and n, and a triangle. m n What is the sum of angles 4, 1, and 5? 2. Name an angle with the same measure as angle 4. Angle 2 3. Name an angle with the same measure as angle 5. Angle 3 4. What is the sum of the measures of angles 1, 2, and 3?

The figure below shows two parallel lines m and n, and a triangle. m n What is the sum of angles 4, 1, and 5? 2. Name an angle with the same measure as angle 4. Angle 2 3. Name an angle with the same measure as angle 5. Angle 3 4. What is the sum of the measures of angles 1, 2, and 3? 180°

Triangle Sum Theorem The angle measures of a triangle add to 180°. ALWAYS!!!

Triangle Review:  Acute triangle  Right triangle  Obtuse triangle  Equilateral triangle  Isosceles triangle  Scalene triangle

Triangle Review:  Acute triangle – 3 acute angles  Right triangle – 1 right angle  Obtuse triangle – 1 obtuse angle  Equilateral triangle – 3 congruent sides 3 congruent angles  Isosceles triangle – 2 congruent sides 2 congruent angles  Scalene triangle – no congruent sides or angles

Classifying Triangles By angles: ______ ________ __________ By sides: _______ ________ _________

Classifying Triangles By angles: AcuteRightObtuse By sides: EquilateralIsoscelesScalene

Finding angle measures – Equilateral Triangle m m m 3m = m = 60°

Finding angle measures – Isosceles Triangle 50 2m + 50 = m = m m m = 65°

Finding angle measures – Scalene Triangle m = m = m = m

Work together (5 min)  Textbook page 208 (1-5)  Answers: 1) q = 77° 2) t = 59° 3) a = 60° 4) c = 56° 5) d = 18°, 4d = 72°, 5d = 90°

Finding angles that meet given conditions: The second angle in a triangle is twice as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure. Let x = first measure Then 2x = second measure, And ½(2x) = third measure. ½(2x) = 1x or x. x + 2x + x = 180

Finding angles that meet given conditions: The second angle in a triangle is twice as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure. x + 2x + x = 180 Combine like terms. 4x = x = 45°

Finding angles that meet given conditions: The second angle in a triangle is twice as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure. Let x = first measure x= 45° Then 2x = second measure, And ½(2x) = third measure. ½(2x) = 1x or x.

Finding angles that meet given conditions: The second angle in a triangle is twice as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure. Let x = first measure x= 45° Then 2x = second measure,2x = 90° And ½(2x) = third measure.x = 45° ½(2x) = 1x or x.

Finding angles that meet given conditions: The second angle in a triangle is twice as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure. x= 45° 45° 2x = 90° x = 45° 45°

You try:  Textbook page 209 (6)  Answer: 60°, 30°, 90°

Remember: Triangle Inequality Theorem (straws) The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Can sides 4, 5, 7 make a triangle? yes Can sides 2, 4, 7 make a triangle? no, because < 7

Check It Out:  Textbook page 209 (7-9)  Answers: 7) No, < 14 8) Yes 9) Yes

Assignment  Textbook page 209 (10-16)  Optional homework: Textbook page 209 (22-29)

Exit slip  Find the missing angle measure a m 63 h 70