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Geometry Unit 4

Geometry Unit 4. Emily Eastman. How to classify triangles. By angle Acute- three acute angles Equiangular- Three cong. Angs . Right- right ang. Obtuse- obtuse ang. By side Equilateral- Three congruent sides Isosceles- At least two congruent sides Scalene- No congruent sides.

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Geometry Unit 4

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  1. Geometry Unit 4 Emily Eastman

  2. How to classify triangles • By angle • Acute-three acute angles • Equiangular-Three cong. Angs. • Right-right ang. • Obtuse-obtuse ang. • By side • Equilateral-Three congruent sides • Isosceles-At least two congruent sides • Scalene-No congruent sides

  3. Theorems about triangles angle relations • Triangle Sum Theorem- The sum of the angles in a triangle is 180 degrees • Third angle Theorem-if 2 angles in one triangle are congruent to two angles of another triangle, the third pair of angles are also congruent

  4. Angles of a Triangle Angles 1, 2, and 3 are interior angles 1 Angle 4 is an exterior angle • In this triangle Angles 1 and 2 are 2 3 4 Remote interior angles • the sum of the measure of the remote interior angles if the measure of the exterior angle

  5. How do we prove triangles congruent? • The Side-Side-Side Postulate, which states if 3 sides on one triangle are congruent to 3 sides of another triangle then the two triangles are congruent. These two triangles are congruent by the SSS Post

  6. How do we prove triangles congruent? • The Side-Angle-Side Postulate-If two sides and the included angles of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent These two triangles are congruent by the SAS Post

  7. How do we prove triangles congruent? • The Angle-Side-Angle Postulate-If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle then the triangles are congruent These triangles are congruent by the ASA Post

  8. How do we prove triangles congruent? • Angle-Angle-Side Theorem-If two angles and the non-included side of a triangle are congruent to two angles and a non-included side of another triangle then the triangles are congruent These triangles are congruent by the ASS theorem

  9. How do we prove triangles congruent? • The Hypotenuse-Leg Theorem states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle then the triangles are congruent These right triangles are congruent by the hypotenuse-leg theorem

  10. *NOTE* • You cannot prove triangles are congruent with ANGLE-ANGLE-ANGLE, or ANGLE-SIDE-SIDE

  11. How do I prove parts of triangles congruent? • If two triangles have already been proven congruent then you can use CPCTC • Congruent • Parts of • Congruent • Triangles are • Congruent

  12. Isosceles triangles • Isosceles triangle theorem-If two sides of a triangle are congruent then the angles opposite those sides are also congruent • Converse of the Isosceles triangle theorem-If two angles of a triangle are congruent then the sides opposite those angles are congruent • The angle bisector of a vertex angles perpendicularly bisects the makes two congruent triangles

  13. Examples • How would you prove these triangles congruent? Answer:Side-Side-Side

  14. How do you prove these triangles congruent? Answer: Side-angle-side postulate Answer:Angle-side-angle postulate

  15. How do you prove these triangles congruent? Answer: Hypotenuse Leg Theorem Answer: Angle Angle Side theorem

  16. How do we prove MN is congruent to BW? Answer: We know the triangles are congruent by ASA and so MN is congruent to BW by CPCTC

  17. Now you’re ready for the test!!

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