Warm Up. 1. If the volume of sphere is equal to 454 cm³ find the radius 2. The circumference of a circle is 24. Find the area of the circle. Unit 1 Part B Review. Congruent Triangles. Congruent triangles have 3 congruent sides and 3 congruent angles.
1. If the volume of sphere is equal to 454 cm³ find the radius
2. The circumference of a circle is 24. Find the area of the circle
Unit 1 Part BReview
Congruent triangles have 3 congruent sides and 3 congruent angles.
The parts of congruent triangles that “match” are called corresponding parts.
In a congruence statement
Everything matches up.
Corresponding Parts of Congruent Triangles are Congruent
If ABC DEF,
then BC ___
If CAT DOG,
then AC ___
Side-Side-Side (SSS) Congruence Postulate
All Three sides in one triangle are congruent to all three sides in the other triangle
Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle
(the angle is in between the 2 marked sides)
Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included
Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side
(the side is in between the 2 marked angles)
NO BAD WORDS
The ONLY Ways To Prove Triangles Are Congruent
Share a side
Reason: reflexive property
Reason: Vertical Angles are congruent
Angle-Angle (AA~) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Side-Angle-Side (SAS~) Similarity THM
If the lengths of two sides are proportional and the included angle is congruent, then the triangles are similar
Side-Side-Side (SSS~) Similarity THM
If the corresponding sides of two triangles are proportional, then the triangles are similar.
Ex. Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement.
Figures that are similar(~) have the same shape but not necessarily the same size.
Have the same size and shape
EXACTALY THE SAME!!!!!
Similar figures have the same shape but not necessarily the same size.
#1 Identify the pairs of congruent angles and corresponding sides
N Q and P R.
By the Third Angles Theorem, M T.
A similarity ratiois the ratio of the lengths of
the corresponding sides of two similar polygons.
The similarity ratio of ∆ABC to ∆DEF is , or .
The similarity ratio of ∆DEF to ∆ABC is , or 2.
Think: What am I multiplying or dividing all sides by to get the lengths of the other triangle?
Also known as the SCALE FACTOR or DIALATION
A 5 ft lady casts a shadow that is 22 ft long. Her son is standing next to her and casts a shadow that is 10 ft long. How tall is her son?