Geometry Section 4-4 1112
Upcoming SlideShare
Loading in...5
×
 

Geometry Section 4-4 1112

on

  • 955 views

Triangle Congruence -- SSS, SAS

Triangle Congruence -- SSS, SAS

Statistics

Views

Total Views
955
Views on SlideShare
501
Embed Views
454

Actions

Likes
0
Downloads
13
Comments
0

1 Embed 454

http://mrlambmath.wikispaces.com 454

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Geometry Section 4-4 1112 Geometry Section 4-4 1112 Presentation Transcript

  • Section 4-4 Proving Congruence: SSS, SASMonday, February 6, 2012
  • Essential Questions How do you use the SSS Postulate to test for triangle congruence? How do you use the SAS Postulate to test for triangle congruence?Monday, February 6, 2012
  • Vocabulary 1. Included Angle: Postulate 4.1 - Side-Side-Side (SSS) Congruence: Postulate 4.2 - Side-Angle-Side (SAS) Congruence:Monday, February 6, 2012
  • Vocabulary 1. Included Angle: An angle formed by two adjacent sides of a polygon Postulate 4.1 - Side-Side-Side (SSS) Congruence: Postulate 4.2 - Side-Angle-Side (SAS) Congruence:Monday, February 6, 2012
  • Vocabulary 1. Included Angle: An angle formed by two adjacent sides of a polygon Postulate 4.1 - Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three corresponding sides of a second, then the triangles are congruent Postulate 4.2 - Side-Angle-Side (SAS) Congruence:Monday, February 6, 2012
  • Vocabulary 1. Included Angle: An angle formed by two adjacent sides of a polygon Postulate 4.1 - Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three corresponding sides of a second, then the triangles are congruent Postulate 4.2 - Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are congruent to two corresponding sides and included angle of a second triangle, then the triangles are congruentMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADUMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AUMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. GivenMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DUMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. ReflexiveMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. Reflexive 3. DU ≅ UDMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. Reflexive 3. DU ≅ UD 3. SymmetricMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. Reflexive 3. DU ≅ UD 3. Symmetric 4. QUD ≅ADUMonday, February 6, 2012
  • Example 1 Prove the following. Given: QU ≅ AD, QD ≅ AU Prove: QUD ≅ADU 1. QU ≅ AD, QD ≅ AU 1. Given 2. DU ≅ DU 2. Reflexive 3. DU ≅ UD 3. Symmetric 4. QUD ≅ADU 4. SSSMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement.Monday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. x yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D x yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D x V yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D x V W yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D x V W yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D x V W L yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D P x V W L yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D P x V W L M yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D P x V W L M yMonday, February 6, 2012
  • Example 2 ∆DVW has vertices D(−5, −1), V(−1, −2), and W(−7, −4). ∆LPM has vertices L(1, −5), P(2, −1), and M(4, −7). Graph both triangles on the coordinate plane. Then, using your drawing, determine whether the triangles are congruent or not, providing a logical argument for your statement. D P x V W These are congruent. What L possible ways could we show this? M yMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIGMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FHMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. GivenMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IGMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpointMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGIMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGI 3. Vertical AnglesMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGI 3. Vertical Angles 4. FEG ≅HIGMonday, February 6, 2012
  • Example 3 Prove the following. Given: EI ≅ FH , G is the midpoint of EI and FH Prove: FEG ≅HIG 1. EI ≅ FH , G is the midpoint of EI and FH 1. Given 2. FG ≅ HG, EG ≅ IG 2. Def. of midpoint 3. ∠FGE ≅ ∠HGI 3. Vertical Angles 4. FEG ≅HIG 4. SASMonday, February 6, 2012
  • Check Your Understanding Review p. 266 #1-4Monday, February 6, 2012
  • Problem SetMonday, February 6, 2012
  • Problem Set p. 267 #5-19 odd, 31, 39, 41 "Doubt whom you will, but never yourself." - Christine BoveeMonday, February 6, 2012