'Sss congruence postulate' diaporamas de présentation

Chapter 4

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Proving Triangles are Congruent SSS, SAS; ASA; AAS

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Proving Triangles are Congruent SSS, SAS; ASA; AAS

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4.5 Using Congruent Triangles

4.5 Using Congruent Triangles. Geometry Mrs. Spitz Fall 2004. Objectives:. Use congruent triangles to plan and write proofs. Use congruent triangles to prove constructions are valid. Assignment:. Pgs. 232-234 #1-21 all. Planning a proof.

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4.3 to 4.5 Proving ? s are ? : SSS, SAS, HL, ASA, & AAS

4.3 to 4.5 Proving ? s are ? : SSS, SAS, HL, ASA, & AAS. Objectives. Use the SSS Postulate Use the SAS Postulate Use the HL Theorem Use ASA Postulate Use AAS Theorem. Postulate 19 ( SSS ) Side-Side-Side ? Postulate.

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Proving ? s are ? : SSS, SAS, HL, ASA, & AAS

Proving ? s are ? : SSS, SAS, HL, ASA, & AAS. SSS Side-Side-Side ? Postulate. If 3 sides of one ? are ? to 3 sides of another ? , then the ? s are ?. E. A. F. C. D. B. More on the SSS Postulate. If AB ? ED, AC ? EF, & BC ? DF, then ? ABC ? ? EDF. Write a proof.

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4.7 Triangles and Coordinate Proof

4.7 Triangles and Coordinate Proof. Objectives:. Place geometric figures in a coordinate plane. Write a coordinate proof. Assignment: 2-26 even. Placing Figures in a Coordinate Plane.

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Warm Up

Complete each statement about parallelogram ABCD. Warm Up. B. A. G. C. D. Section 8.3 (a) Show that a Quadrilateral is a Parallelogram. Quadrilateral. Both pairs of opposite sides are parallel. Parallelogram. Opposite sides are congruent. Opposite angles are congruent.

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SSS AND SAS C ONGRUENCE P OSTULATES

SSS AND SAS C ONGRUENCE P OSTULATES. then. If. 1. AB DE. 4. A D. 2. BC EF. 5. B E. ? ABC ? DEF. 3. AC DF. 6. C F. If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Sides are congruent. Angles are congruent.

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GEOMETRY: Chapter 4

GEOMETRY: Chapter 4. 4.3: Prove Triangles Congruent by SSS and SAS. Postulate 19: Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

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EXAMPLE 3

ALGEBRA. Find the values of x and y in the diagram. STEP 1. Find the value of y . Because KLN is equiangular, it is also equilateral and KN KL . Therefore, y = 4. STEP 2.

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EXAMPLE 3

ALGEBRA. Find the values of x and y in the diagram. STEP 1. Find the value of y . Because KLN is equiangular, it is also equilateral and KN KL . Therefore, y = 4. STEP 2.

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4.8

4.8. Prove Triangles Congruent by SSS. B. S. T. C. R. A. Side-Side-Side (SSS) Congruence Postulate. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. 4.8. Prove Triangles Congruent by SSS. D. A. E. B. C.

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EXAMPLE 3

EXAMPLE 3. Find the orthocenter. Find the orthocenter P in an acute, a right, and an obtuse triangle. SOLUTION. Right triangle P is on triangle. Acute triangle P is inside triangle. Obtuse triangle P is outside triangle.

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EXAMPLE 3

EXAMPLE 3. Find the orthocenter. Find the orthocenter P in an acute, a right, and an obtuse triangle. SOLUTION. Right triangle P is on triangle. Acute triangle P is inside triangle. Obtuse triangle P is outside triangle.

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EXAMPLE 1

Write a proof. GIVEN. KL NL , KM NM. PROVE. KLM NLM. Proof. KL NL and KM NM. It is given that. LM LN . By the Reflexive Property,. So, by the SSS Congruence Postulate,. KLM NLM. EXAMPLE 1. Use the SSS Congruence Postulate. DFG HJK.

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EXAMPLE 4

GIVEN. AB DE , A C DF , BC EF. D A. PROVE. Add BC and EF to the diagram. In the construction, AB , DE , AC , and DF are all determined by the same compass setting, as are BC and EF . So, you can assume the following as given statements. EXAMPLE 4.

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4.4

4.4. Prove Triangles Congruent by SSS. B. S. T. C. R. A. Side-Side-Side (SSS) Congruence Postulate. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. 4.4. Prove Triangles Congruent by SSS. D. A. E. B. C.

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