1 / 22

Exploring Isosceles Triangles

Learn about the properties of isosceles triangles, the sum of angle measures in a triangle, and how to prove the Triangle Sum Conjecture. Practice solving problems and identifying isosceles triangles.

genem
Download Presentation

Exploring Isosceles Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Do Now • Take out your compass and a protractor. • Look at the new seating chart and find your new seat. • Classify this triangle: • By angles • By side lengths • On a piece of paper draw a triangle. (It can be acute, right, or obtuse.) Make it big enough to measure the angles.

  2. Isosceles Triangles

  3. TODAY’S OBJECTIVES • Discover the relationship between the base angles of an isosceles triangle. • Explain the sum of the measures of the angles of a triangle. • Write a paragraph proof. • Use problem solving skills.

  4. YOU MAY ASSUME THAT… • Lines are straight • If two lines intersect, they intersect at a point.

  5. DO NOT ASSUME THAT… • Lines are parallel unless they are marked parallel, even if they “look” parallel • Lines are perpendicular unless they are marked perpendicular, even if they “look” perpendicular • Pairs of angles, segments, or polygons are congruent unless they are marked congruent, even if they “look” congruent.

  6. The triangle sum: Investigation • On a piece of paper, draw a triangle. (Make sure your group has at least one obtuse and one acute triangle.) • Measure all three angles as accurately as possible. • Find the sum of the measures of the three angles. Compare with your group. • Mark your angles A, B, and C. Cut out the triangle. • Tear off the three angles. Arrange them so their vertices meet at a point. How does this arrangement show the sum of the angle measures?

  7. Triangle Sum Conjecture • The sum of the measures of the angles in every triangle is___. • 180o . • Based on what type of reasoning? • Inductive. • Can we prove it using deductive reasoning? • Let’s prove it!

  8. Proof of Triangle Sum Conjecture • As a group, explain why the Triangle Sum Conjecture is true by writing a paragraph proof (a deductive argument that uses written sentences to support its claims with reasons). • Hints to get started: • What are you trying to prove? • How are the angles related? • Mark your diagram. • How can you use the information you have to prove that the Triangle Sum Conjecture is true for every triangle? • Remember what you can and cannot assume.

  9. Practice • Solve for p and q.

  10. Properties of Isosceles Triangles • Two sides are congruent

  11. Base Angles in an Isosceles Triangle: Investigation • Draw an angle. Label it C. This will be the vertex angle of your isosceles triangle. • Place a point A on one ray. Using your compass, copy segment CA onto the other ray and mark point B so that CA=CB. • Draw AB. • How do you know ΔABC is isosceles? • Name the base and the base angles. • Use your protractor to measure the base angles. What do you notice?

  12. Isosceles Triangle Conjecture • If a triangle is isosceles, then ____________________________. • it’s base angles are congruent. • Is the converse true? • Let’s find out.

  13. Converse: Investigation • Draw a segment and label it AB. Draw an acute angle at A. • Copy A at point B on the same side of the segment. • Label the intersection of the two rays point C. • Use your compass to compare the lengths of AC and BC. What do you notice?

  14. Converse of the Isosceles Triangle Conjecture • If a triangle has two congruent angles, then _______________. • it is an isosceles triangle.

  15. Practice • Find the measure of T.

  16. Stations • Collaborative: Start your group project. • Independent: Get familiar with McGraw Hill • Direct: Practice.

  17. What’s wrong with this picture? • A

  18. Practice • Solve for r, s and t.

  19. Practice • The perimeter of ΔQRS is 344. • mQ= • QR=

  20. TODAY’S OBJECTIVES • Discover the relationship between the base angles of an isosceles triangle. • Explain the sum of the measures of the angles of a triangle. • Write a paragraph proof. • Use problem solving skills.

  21. Exit Slip For each question, show your work and explain your reasoning. • Find x (above). • mA= • a= • The perimeter of ΔABC=

  22. Honors Exit Slip • Find x (above). Explain your reasoning. • mA= • The perimeter of ΔABC= • Use the diagram below to explain why ΔPQR is isosceles.

More Related