4/27

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

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

Good Things

Recap of yesterday…. Triangle Proportionality Theorem Triangle Bisector Theorem

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

Perpendicular Bisector Theorem 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! Hint: draw them separately

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

Guided Practice Triangle ACB ~ Triangle CDB ~ Triangle ADC

Partner Practice Solve for x

Guided Notes!!! Complete the worksheet using the following BlendSpace link: https://www.tes.com/lessons/oy1-mDSbFWmyHQ/4-27-unit-4- guided-notes OR http://bit.ly/2q8AZYL Each section on the Blendspace matches a section on your paper This is due at the end of class! You do NOT need sound for the video – just follow along

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

Congruence Postulates SAS (Side – Angle– Side) Two sides and the included angle are equal https://www.geogebra.org/m/bM5FkyFK https://www.geogebra.org/m/bM5FkyFK

Congruence Postulates ASA (Angle - Side – Angle) Two angles and the included side are equal. https://www.geogebra.org/m/WKJJ2uPa https://www.geogebra.org/m/WKJJ2uPa

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

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

Angle Relationships Supplementary angles add up to 180o These are types of angles that we should already know Supplementary angles add up to 180o Hint: form a straight line (also called a straight angle) Complementary angles add up to 90o Hint: 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 A bisector is a line that cuts something in half 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 Bisector bottom parts of both triangles hypotenuse of both triangles