1 / 16

Chapter 4 Test

Chapter 4 Test. Important Topics By Tiffany Amoroso and Killian McGinnis. Classifying Triangles. By side lengths Equilateral: A triangle with three congruent sides Isosceles : A triangle with at least two congruent sides Scalene: A triangle with no congruent sides By angles

nardo
Télécharger la présentation

Chapter 4 Test

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. Chapter 4 Test Important Topics By Tiffany Amoroso and Killian McGinnis

  2. Classifying Triangles • By side lengths • Equilateral: A triangle with three congruent sides • Isosceles : A triangle with at least two congruent sides • Scalene: A triangle with no congruent sides • By angles • Acute: A triangle with three acute angles • Equiangular: Three congruent angles in a triangle • Obtuse: A triangle with one obtuse angle • Right: A triangle with one right angle

  3. Triangle Sum Theorem • The sum of the angles of a triangle equals 180˚.

  4. Auxiliary Line • A line that is added to a figure to aid in proof

  5. Types of Angles in a Triangle • Interior Ingles – the set of all points inside the figure; formed by 2 sides of a triangle • Exterior Angles – the set of all points outside the figure; formed by one side of the triangle and the extension of an adjacent side • Remote Interior Angles – angle that is not adjacent to the exterior angle; an exterior angle has 2 remote interior angles

  6. Theorems • Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. • Third Angles Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent.

  7. Theorems to prove triangles congruent

  8. SSS Postulate If three sides of one triangle are congruent to three sides on another triangle, then the triangles are congruent △ABC ≅ △XWY by the SSS Postulate

  9. SAS Theorem If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent △BOW ≅ △MAN by the SAS Theorem

  10. ASA Theorem If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent △ABC ≅ △DEF by the ASA Theorem

  11. AAS Theorem If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent △BOW ≅ △MAN by the AAS Theorem

  12. H-L Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent △BOW ≅ △MAN by the H-L Theorem

  13. CPCTC orresponding arts of △BOW ≅ △MAN by the SAS Theorem ongruent ∠N ≅ ∠W by CPCTC riangles are ongruent ** CPCTC can only be used to prove parts of triangles congruent after the triangles have been proven congruent **

  14. Isosceles Triangle Vertex Angle Leg Leg Base Base Angles

  15. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent

  16. Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those are congruent

More Related