427 427 Do Now Essential Question How can

+ 4/27

+ 4/27 Do Now Essential Question: How can I use proportions to solve for the missing side of a triangle?

+ Agenda n Do Now n Good Things n Recap: n n Triangle Proportionality Theorem n Triangle Angle Bisector Theorem Notes: n Perpendicular Bisector Theorem

+ Good Things

+ Recap of yesterday…. n Triangle Proportionality Theorem n Triangle Bisector Theorem

+ Group Warm Up Find the length of side BC Find the length of sides BC and CD

+ Perpendicular Bisector Theorem n Altitude – line that connects a vertex to the base and is perpendicular to the base The altitude creates 2 other right triangles – BDC and ADC Perpendicular means 90 degrees Triangle ADC ~ Triangle ACB are similar through AA!

+ Guided Practice Use corresponding sides to write a proportion with “x” Cross multiply to solve for x!

+ Guided Practice Triangle ACB ~ Triangle CDB ~ Triangle ADC

+ Partner Practice n Solve for x

+ Guided Notes!!! n Complete the worksheet using the following Blend. Space link: n https: //www. tes. com/lessons/oy 1 -m. DSb. FWmy. HQ/4 -27 -unit-4 guided-notes n OR http: //bit. ly/2 q 8 AZYL n Each section on the Blendspace matches a section on your paper n This is due at the end of class! n You do NOT need sound for the video – just follow along

+ Congruence Postulates n SSS n All (Side – Side) 3 sides equal

+ Congruence Postulates n SAS (Side – Angle– Side) n Two sides and the included angle are equal https: //www. geogebra. org/m/b. M 5 Fky. FK

+ Congruence Postulates n ASA (Angle - Side – Angle) n Two angles and the included side are equal. https: //www. geogebra. org/m/WKJJ 2 u. Pa

+ Congruence Postulates n AAS (Angle – Side) n Two angles and the non-included side are equal.

+ Congruence Postulates n ONLY n HL WORKS FOR RIGHT TRIANGLES****** (Hypotenuse – Leg) n Same length of hypotenuse n Same length for one of the other legs

+ Angle Relationships These are types of angles that we should already know n Supplementary n Hint: angles add up to 180 o form a straight line (also called a straight angle) n Complementary n Hint: angles add up to 90 o form a right angle

+ Triangle Sum Theorem The three interior angles of a triangle always add up to 180 degrees.

+ Exterior Angle Theorem <A = <C + <D The exterior angle is equal to the sum of the remote interior angles.

+ Notes: Isosceles Triangles The base angles of an isosceles triangle are congruent The legs of an isosceles triangle are congruent

+ Triangle Midsegment Theorem A midsegment of a triangle is parallel to the base and is half as long as the base. ___ AC || XY ___ XY = ½ * AC

+ Triangle proportionality theorem In this figure According to this theorem, *the arrows in the middle tell us that these lines are parallel Left Short / Left Long = Right Short / Right Long

+ Triangle Angle Bisector Theorem n. A bisector is a line that cuts something in half n If an angle of a triangle is bisected (cut in half), the bisector divides the opposite side of the triangle into two segments that are proportional to the other two sides of the triangle bottom parts of both triangles hypotenuse of both triangles Bisector