Stuck on 4.1 – 4.4?

1. Stuck on 4.1 – 4.4? Katalina Urrea and Maddie Stein ;)

2. Vocabulary • Base angle- angles whose vertices are the endpoints of the base • Base of an isosceles triangle- the angles whose vertices are the endpoints of the base of an isosceles triangle • CPCTC- Abbreviation for “corresponding parts of congruent triangles are congruent” • Corollary- A theorem that follows directly from another theorem and that can easily be proved from that theorem • Isosceles triangle- A triangle with at least two congruent sides • Legs of an isosceles triangle- The two congruent sides of an isosceles triangle • Vertex angle- The opposite angles formed by two intersecting lines.

3. 4.1 Congruent Polygons

4. Polygon Congruence Postulate • Two polygons are congruent IFF (if and only if) there is a correspondence between their sides and angles such that: -Each pair of corresponding angles are congruent -Each pair of corresponding sides are congruent • (Converse is true as well)

5. Naming Polygons • You must name polygons in order • The name of this polygon is ABCDEF • You can also name it BCDEFA, CDEFAB and so on, but you MUST keep it in order.

6. Side and Angle Congruence ABCD EFGH Sides: Angles: AB EF <A <E BC FG <B <F CD GH <C <G DA HE <D <H

7. 4.2Triangle Congruence

8. Side-Side-Side Postulate (SSS) • If the sides of one triangle are congruent to the sides of another triangle then those triangles are congruent.

9. Given: ABCD is a rhombus Prove: ABD DBC Statements Reasons ABCD is rhombus Given AB BC CD DA Definition of Rhombus BD BD Reflexive ABD DBC SSS

10. Side-Angle-Side Postulate (SAS) • If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then those two triangles are congruent.

11. Given: AB//CD AB CD Prove: ABD CBD StatementsReasons AB//CD AB CD Given <BDC <ABD Alternate Interior Angle DB DB Reflexive ABD CBD SAS

12. Angle-Side-Angle Postulate (ASA) • If two angles and the included side of a triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.

13. Given: <A <E AC CE Prove: ABC CDE StatementsReasons <A <E AC CE Given <ACB <DCB Vertical Angles ABC CDE ASA

14. 4.3

15. Angle-Angle-Side Theorem (AAS) • If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.

16. Given: AD AE <C <B Prove: BAD CAE Statements Reasons AD AE <C <B Given <DAB <EAC Reflexive BAD CAE AAS

17. HL (Hypotenuse-Leg) Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.

18. Given: ABC is isosceles BD perpendicular CA Prove: ABD CBD Statements Reasons ABC is isosceles Given BD perpendicular CA Given AB BC Definition of Isosceles <BDA= 90° Definition of Perpendicular <BDC=90° Definition of Perpendicular <BDA <BDC Transitive BD BD Reflexive ABD CBD

19. 4.4Isosceles Triangles

20. Isosceles Triangle Theorem (Base Angle Theorem) • If two sides of the triangle are congruent, then the two angles opposite those sides are congruent. • The converse is also true.

21. Given: AB BC Prove: <A <B StatementsReasons AB BC Given DB is an angle bisector Construction <ABD <CBD Definition of Angle Bisector DB DB Reflexive ABD CBD SAS <A <B CPCTC

22. Corollaries • The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. 2) The measure of each angle in an equilateral triangle is 60°.

23. http://www.washoe.k12.nv.us/ecollab/washoemath/dictionary/vmd/full/s/side-side-sidesss.htmhttp://www.washoe.k12.nv.us/ecollab/washoemath/dictionary/vmd/full/s/side-side-sidesss.htm • http://www.ekacademy.org/mines/hspe/CreateHtm/htm/4-8-2_n-nevadan-4-2-3-1.htm