12. if ea=4, he=8, and er=5. find ht?

13. determine if the sides are proportional. if so prove thag sur ~eup.

someone me with both

12. HT = 15

13. Ratios are equal and triangles are similar.

Step-by-step explanation:

Problem 12.

Because of the parallel lines, triangles AER and AHT are similar. EA = 4, and HE = 8. EA + HE = HA = 12.

EA/HA = ER/HT

4/12 = 5/HT

4HT = 12 * 5

HT = 3 * 5

HT = 15

Problem 13.

EU/SU = 6/15 = 2/5

PU/UR = 8/20 = 2/5

Since the ratios above are equal, the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of the other triangle. The included angles are congruent since they are vertical angles. By SAS Similarity, the triangles are similar.

HT = 15

Step-by-step explanation:

HA = HE + EA = 8 + 4

So

EA/HA = ER/HT

HT = HA * ER / EA

HT = 12 * 5/4

HT = 15

Answer

HT = 15

a

step-by-step explanation: