5-4 Congruent Triangles

Congruent Triangles An Introduction to Corresponding Parts

Two figures are congruent if they are the same size and same shape.

Congruent figures can be rotations of one another.

Congruent figures can be reflections of one another.

∆ABC is congruent to ∆XYZ AB C XY Z

AB C XY Z Corresponding parts of these triangles are congruent.

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. Corresponding parts are angles and sides that “match.”

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. AX

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. BY

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. CZ

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. ABXY

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. BCYZ

∆ABC is congruent to ∆XYZ AB C XY Z Corresponding parts of these triangles are congruent. ACXZ

∆DEF is congruent to ∆QRS DE F Q R S

DE F Q R S Corresponding parts of these triangles are congruent.

∆DEF is congruent to ∆QRS DE F Q R S Corresponding parts of these triangles are congruent. DQ

∆DEF is congruent to ∆QRS DE F Q R S Corresponding parts of these triangles are congruent. ER

∆DEF is congruent to ∆QRS DE F Q R S Corresponding parts of these triangles are congruent. FS

∆DEF is congruent to ∆QRS DE F Q R S Corresponding parts of these triangles are congruent. DEQR

∆DEF is congruent to ∆QRS DE F Q R S Corresponding parts of these triangles are congruent. DFQS

∆DEF is congruent to ∆QRS DE F Q R S Corresponding parts of these triangles are congruent. FESR

Practice Time!

1) Are these shapes congruent? Explain.

These shapes are congruent because they are both parallelograms of equal size.

2) Are these shapes congruent? Explain.

These shapes are not congruent because they are different sizes.

3) Are these shapes congruent? Explain.

These shapes are congruent because they are the same size.

4) ∆BAD is congruent to ∆THE B A DE TH Name all corresponding parts.

4) ∆BAD is congruent to ∆THE B A DE TH Name all corresponding parts. ANGLESSIDES BATH ADHE DBET BT AH DE

5) ∆FGH is congruent to ∆JKL G F H J KL Name all corresponding parts.

5) ∆FGH is congruent to ∆JKL G F H J KL Name all corresponding parts. ANGLESSIDES FGJK GHKL HFLJ FJ HL GK

6) ∆QRS is congruent to ∆BRX B R Q S X Name all corresponding parts.

6) ∆QRS is congruent to ∆BRX B R Q S X Name all corresponding parts. ANGLESSIDES QRBR QSBX SRXR QB SX RR

7) ∆EFG is congruent to ∆FGH H G F E Name all corresponding parts.

7) ∆EFG is congruent to ∆FGH H G F E Name all corresponding parts. ANGLESSIDES EFHF EGHG GF EH FF GG

1-1A Slide 1 of 3

1-2A Slide 2 of 2

1-2B Slide 2 of 2

1-2C Slide 2 of 2

1-2D Slide 2 of 2

1-2E Slide 2 of 2

1-2F Slide 2 of 2

1-2G Slide 2 of 2

1-2a Slide 2 of 2 (over Lesson 5-4)

1-2b Slide 2 of 2 (over Lesson 5-4)

In the figure, quadrilateral JIHK quadrilateral QRST. Find a. 3a3a 4b° 6 30° Q 120° R S H I J K 3a = a = 2 c + 10° T 3a = 6 IH RS Divide both sides by 3.

In the figure, quadrilateral JIHK quadrilateral QRST. 3a3a 4b° 6 30° Q 120° R S H I J K c + 10° T Divide both sides by b = 120 H S b = 30° Find b.

In the figure, quadrilateral JIHK quadrilateral QRST. Find c. Subtract 10 from both sides. –10 c + 10 = 30 K T 3a3a 4b° 6 30° Q 120° R S H I J K c + 10° T c = 20°

Congruent Triangles THE END