Question

tell whether the triangles are congruent. explain your reasoning. 1. 2. describe a sequence of transformations that proves the figures are congruent. 3. 4. find the value of the variables that results in congruent triangles. 5. 6. journal and practice work

Explanation:

for 1:

Step1: Calculate ABC's third angle

180°-75°-80°=25°

Step2: Calculate DEF's third angle

180°-75°-80°=25°

Step3: Compare sides

AC=DF=1.5, BC=EF=3.3, AB=DE=3.4

for 2:

Step1: Calculate MNP's third angle

180°-24°-56°=100°

Step2: Calculate JKL's third angle

180°-24°-108°=48°

Step3: Check angle congruence

100°≠48°, angles not matching

for 5:

Step1: Equate corresponding angles

5x+23=8x-1

Step2: Solve for x

3x=24 → x=8

for 6:

Step1: Equate corresponding sides

5x+11=7x-3

Step2: Solve for x

2x=14 → x=7

Answer:

for 1: Congruent (SSS/ASA)