Triangle Midsegment A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle In the figure D is the midpoint of AB and E is the midpoint of AC. So, DE is a midsegment.

Triangle Midsegment Theorem A midsegment connecting two sides of a triangle is parallel to the third side and is half as long. If AD = DB and AE = EC, then DE II BC and DE = ½BC

Congruent Polygons Goal: To identify corresponding parts of CONGRUENT figures.

Congruent (  ) Geometric figures that have the SAME SIZE and SHAPE are congruent. LINE segments are congruent if they have the SAME LENGTH ANGLES are congruent if they have the same DEGREE MEASURE.

Congruent Polygons Polygons are congruent when there is a way to match up their vertices so that all pairs of CORRESPONDING ANGLES and all pairs of CORRESPONDING SIDES are CONGRUENT.

Congruent Polygons Triangle ABC and Triangle PQR are congruent Triangles

Congruent Polygons Use the figures to complete each statement. PQ  ____  C  ____ ABC  ______ If the length of AB is 8 cm., then the length of _____ is also 8 cm. If m  A = 50°, then the m  P = ______

Congruent Polygons Are these triangles congruent?

IDENTIFY CONGRUENCE TRANSFORMATIONS B A C B A C If you slide ΔABC down and to the right, it is still congruent to ΔDEF. E D F

IDENTIFY CONGRUENCE TRANSFORMATIONS B A C B A C If you turn ΔABC, it is still congruent to ΔDEF. E D F

IDENTIFY CONGRUENCE TRANSFORMATIONS B A C B A C If you flip ΔABC, it is still congruent to ΔDEF. E D F

Congruent Polygons Use the figures to complete each statement. BC  ____  D  ____ Polygon ABCD  ______

The support beams on the fence form congruent triangles. Name the corresponding congruent angles and sides of  ABC and  DEF.

Use the figure at the right to complete each statement.  H  ____  B  ____  D  ____ DE  ____ GF  ____ AE  ____ Pentagon ABCDE  _________ H G F B C D A E

Jim Smith JCHS Sections 4-2, 4-3, 4-5

When we talk about congruent triangles, we mean everything about them Is congruent. All 3 pairs of corresponding angles are equal…. And all 3 pairs of corresponding sides are equal

For us to prove that 2 people are identical twins, we don’t need to show that all “2000” body parts are equal. We can take a short cut and show 3 or 4 things are equal such as their face, age and height. If these are the same I think we can agree they are twins. The same is true for triangles. We don’t need to prove all 6 corresponding parts are congruent. We have 5 short cuts or methods.

SSS If we can show all 3 pairs of corr. sides are congruent, the triangles have to be congruent.

SAS Show 2 pairs of sides and the included angles are congruent and the triangles have to be congruent. Includedangle Non-includedangles

This is called a common side. It is a side for both triangles. We’ll use the reflexive property.

Which method can be used to prove the triangles are congruent

Common side SSS Parallel lines alt int angles Common side SAS Vertical angles SAS

ASA, AAS and HL ASA – 2 angles and the included side A S A AAS – 2 angles and The non-included side AA S

HL ( hypotenuse leg ) is used only with right triangles, BUT, not all right triangles. HL ASA

Can you prove this triangles are congruent?

Pythagorean Theorem

Proving Triangles Congruent MathScience Innovation Center B. Davis

Proving Triangles Congruent B. Davis MathScience Innovation Center Corresponding Parts Given ABC, name the congruent A X C Y Z B Is it XYZ, ZXY, or YZX ?

Proving Triangles Congruent B. Davis MathScience Innovation Center Corresponding Parts Given ABC, name all 6 parts. A C B Three angles! And 3 sides !

Proving Triangles Congruent B. Davis MathScience Innovation Center Proving Triangles Congruent Decide the reason why these triangles may be congruent. Choices: SSS SAS ASA AAS None

Proving Triangles Congruent B. Davis MathScience Innovation Center Proving Triangles Congruent Decide the reason why these triangles may be congruent. Choices: SSS SAS ASA AAS None

Proving Triangles Congruent B. Davis MathScience Innovation Center Proving Triangles Congruent Decide the reason why these triangles may be congruent. Choices: SSS SAS ASA AAS None

Proving Triangles Congruent B. Davis MathScience Innovation Center Proving Triangles Congruent Decide the reason why these triangles may be congruent. Choices: SSS SAS ASA AAS None