Bell Work 112812 Classify each triangle using angles

Bell Work 11/28/12 • Classify each triangle using angles and sides. • 1) 2) • Write an equation for a line with the following: • 3) parallel to: 4) perpendicular to: y = 3 x – 4; y-int at 5 y = -1/2 x + 4 through (2, 1)

Outcomes • I will be able to: • 1) Identify congruent figures and their corresponding parts • 2) Prove that two triangles are congruent • 3) Write a congruence statement

Congruence • What does it mean for two figures to be congruent? • Congruence Investigation: • 1) Open Geometry Pad • 2) Plot each triangle • 3) Find the measure of the angles and sides • 4) Determine if the triangles are congruent • 5) Decide what it means for figures to be congruent

Congruent Figures Two figures are congruent if they have the exact same size and shape The corresponding parts of congruent triangles are always congruent. So,

Congruence Statement • Congruence Statement: A symbolic statement in which we write what figures are congruent. • ***Be sure corresponding parts line up!!!

Congruent Figures Example 1 a

Congruent Figures Example 1 b • Circle the figures that look congruent

Congruent Figures Example 2 Remember, corresponding parts must be congruent!!!

Congruent Figures Example 3 What do we know about angle A and angle D? What do we know about angle B and E? So, how can we solve for x? 5 x + 2 = 87 How can we solve for y? 87 + 42 + 3 y = 180 5 x = 85 3 y = 51 x = 17 y = 17

Third Angles Theorem If two angles of one triangle are congruent to two angles in another triangle, then the third angles are congruent. Angle A = 57 Angle D 57 Angle B = 90 Angle E = 90 Angle C = x Angle F = 33 Without doing any math, how can we find C? x = 33

Third Angles Example 1 55 + 65 + 2 x + 30 = 180 2 x = 30 x = 15 What do we know about M and T? They are congruent How can we find x?

Quiz Friday • Quiz will cover: • 1) Writing equations of parallel and perpendicular lines • 2) Determining if two lines are parallel • 3) Solving for variables in parallel lines • 4) Classifying triangles

White Board Quiz Review • 1) Find the variables • X = 12 • Y = 11

White Board Quiz Review • 2) Write an equation of the line parallel to: • y = 1/4 x – 5 with a y-intercept of -11 • y = 1/4 x -11

White Board Quiz Review • 3) Write an equation of the line perpendicular to: y = 1/3 x + 4 through (-1, 5) • (y – 5) = -3(x + 1) • or y = -3 x + 2

White Board Quiz Review • 4) Are the lines parallel? Explain why/why not • Yes, corresponding angles are congruent

White Board Quiz Review • 5) Are the lines parallel? Explain why/why not. • No, same side interior angles are congruent. They should add to 180°.

White Board Quiz Review • 6) Write the equation of the line parallel to: y = 1/5 x + 10 through (0, -5) • (y + 5) = 1/5(x – 0) • or y = 1/5 x - 5

White Board Quiz Review • 7) Are the lines parallel? Explain why/why not. • No, same side interior angles do not add to 180°

White Board Quiz Review • 8) Classify the following triangle using its sides and angles • Acute Scalene Triangle

White Board Quiz Review • 9) Classify the following triangle using its sides and angles. • Right Scalene Triangle

White Board Quiz Review • 10) Classify the following triangle using its sides and angles • Equiangular equilateral triangle • Could also be classified as isosceles or acute

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