Warm-up Take a copy of the white paper and get busy!!!

Warm-up

Warm-up fi yuo cna raed tihs, yuo hvae a sgtrane mnid too Cna yuo raed tihs? i cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it dseno't mtaetr in waht oerdr the ltteres in a wrod are, the olny iproamtnt tihng is taht the frsit and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it whotuit a pboerlm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Azanmig huh? yaeh and I awlyas tghuhot slpeling was ipmorantt!

Agenda Homework Review Section 5-4 Section 5-5 Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-3 Study Guide Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

Given: Points A, B and C are on line l Point P is not on l PB < PC Prove: mPCB  90 A B C l 1. 2. 3. 4. P

Given: Points A, B and C are on line l Point P is not on l PB < PC Prove: mPCB  90 A B C l Assume PCB = 90 Then PC  l  PC < PB (Contradiction)  PCB  90 P

4

5-4 Side & Angle Inequalities Theorem 5-9 If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

5-4 Side & Angle Inequalities Theorem 5-10 If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

5-4 Side & Angle Inequalities Theorem 5-11 The perpendicular segment from a point to a line is the shortest segment from the point to the line.

5-5 Triangle Inequalities Build a triangle Get rulers and plain paper Draw ABC where AC = 10 in and AB = 6 in and BC = 4 in

Section 5-4 14 16 7 7 22 22

Section 5-4

5-5 Triangle Inequalities If two sides of a triangle are 5 and 12 what are the possible values for the size of the third side?

Theorem 5-13 SAS Inequality Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the third side of the first triangle is longer than the third side in the second triangle.

Theorem 5-14 SSS Inequality If two sides of one triangle are congruent to two sides of another triangle and the third side in the first triangle has a greater measure than the third side in the other, then the angle between the pair of congruent sides in the first triangle is larger than the included angle in the second triangle.

Example

Examples

Examples

Given: mP > mR Prove: m2 > m1 1. 1. 2. 2. 3. 3. 4. 4. 5. 5.

Given: mP > mR Prove: m2 > m1 1. 1. Given 2. Reflexive property 2. 3. 3. Given 4. 4. Larger  implies larger side 5. 5. SSS Inequality

Answers Ahead

5-4 Study Guide Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-4 Study Guide Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-4 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

5-4 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

Homework Study Guide & Practice 5-4 Study Guide & Practice 5-5