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Chapter 4 – Triangle Congruence Terms, Postulates and Theorems 4.1 Scalene triangle - A triangle with all three sides having different lengths. Equilateral triangle - All sides of a triangle are congruent. Isosceles triangle - A triangle with at least two sides congruent. • Legs of an isosceles triangle - The congruent sides
TRIANGLE CONGRUENCE POSTULATES Mark the following triangles given the stated congruent triangle postulate. DEF SSS SAA E D ASA SAS Determine which triangles are congruent and why? Using your previous postulates mark congruent angles and sides if they exist and then find the corresponding congruent triangle.
Introduction to proofs: Identifying geometry theorems and postulates C congruent ? Explain using geometry concepts and theorems: 1) Why is the triangle isosceles? 2) Why is an altitude? 3) Why are the triangles congruent? 4) Why is NM a median? 5) If ABCD is a parallelogram, why are LA and 6) Why are the triangles congruent?
The sides are DE, EF, and DF. The vertices are D, E, and F. The angles are D, E, and F. In Chapter 3, you classified angles as acute, obtuse, or right. Triangles can also be classified by their angles. All triangles have at least two acute angles. The third angle is either acute, obtuse, or right.
Give the postulate or theorem that proves the triangles congruent (SSS, SAS, ASA, AAS, HL) . Finally, fill in the blanks to complete the proof. 1. Given: BC ≅ DC ; AC ≅ EC Prove: ΔBCA ≅ ΔDCE. 2. Given: JK ≅ LK ; JM ≅ LM Prove: ΔKJM ≅ ΔKLM. 3. Given: ∠G ≅ ∠I ; FH bisects ∠GFI Prove: ΔGFH ≅ ΔIFH. B D. C. A E.
Angle – Side – Angle Postulate (ASA): 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.
Right Triangle Congruence Date_____ Period____ State if the two triangles are congruent. If they are, state how you know. 1) LL 2) HL 3) HA 4) HA 5) HA 6) Not congruent 7) Not congruent 8) LL 9) Not congruent 10) LL-1-