1 / 8

Applying Congruent Triangles

Applying Congruent Triangles. OBJECTIVES. Special segments in triangles Congruence with right triangles Inequalities in triangles Relationship of sides and angles in a triangle. 3 Medians—from vertex to midpoint of opposite side

lucia
Télécharger la présentation

Applying Congruent Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applying Congruent Triangles OBJECTIVES Special segments in triangles Congruence with right triangles Inequalities in triangles Relationship of sides and angles in a triangle

  2. 3 Medians—from vertex to midpoint of opposite side 3 Altitudes—from vertex to opposite side, hitting it at a 90°angle (can be outside if it’s an obtuse Δ) 3 Angle bisectors—bisects the angle & hits side opposite 3 Perpendicular bisectors—bisects side at 90 °angle Special segments in triangles

  3. Perpendicular bisectors: Any point on the perpendicular bisector is equidistant from endpoints of the segments ( & ‘vice versa’) Angle bisectors: Any point on the angle bisector is equidistant from the sides of the angle (& ‘vice versa’) Properties of Bisectors

  4. Right triangles LEG HYPOTENUSE LEG LL: IF the legs of one right Δ are to the corresponding legs of another rt. Δ … HA: IF the hypotenuse & an acute angle of one right Δ are to the hyp. & acute angle of a 2nd rt.Δ … LA: IF one leg and an acute angle of 1 rt. Δ are to the corr. leg and acute angle of a 2nd rt. Δ … HL: IF the hyp.& a leg of 1 rt. Δ are to the hyp. & corr. leg of a 2nd rt. Δ…  …THEN THE Δ’S ARE CONGRUENT

  5. 1. Assume the conclusion is false. 2. Show that it leads to a contradiction or an impossible statement (type of working backwards to solve). 3. Point out the assumption (#1) must be incorrect the conclusion is really true. Inequalities Definition: a > b iffthere is some positive number c such that a = b + c Indirect Proof

  6. Inequalities -The Exterior Angle is > sum of 2 remote interior angles -If one side of aΔ is longer than another, then the opp the longer side > the opp the shorter side. -If an of a Δ is > another, the side opp the greater will be longer than the side opp the smaller -The | segment from a point to a line is the shortest distance(segment) from the pt to the line -The | segment from a point to a plane is the shortest distance (segment) from the pt to the plane.

  7. Triangle Inequalities The sum of the lengths of any two sides of a Δ is greater than the 3rd side. The smallest side of the Δ is opposite the smallest and the largest side is opposite the largest

  8. Example: Triangle Inequality If two sides of a triangle are 7 & 13, between what two numbers must the third side be? -if 13 is the largest side then the smallest side had to be > 6 (13 < 7 + ? ) -If 7 & 13 are the 2 smaller sides, the 3rd side has to be < 20 (? < 13 + 7 ) Answer: the 3rd side is between 6 and 20.

More Related